publications

2026

1. arXiv e-prints

   Indefinite Quantum Causality

   F. Costa, G. Rubino, C. Branciard, Č. Brukner, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   In recent years, operational approaches to quantum foundations have been developed as a means of understanding the core principles and distinctive features of quantum theory. Such approaches typically view physical processes as sequences of operations, with earlier operations serving as causes of later effects. However, a growing literature is emerging on the possibility of relaxing this assumption and allowing for quantum indefiniteness in the causal order. This development stems from a variety of motivations, both fundamental and applied, including exploring the role of causality in quantum theory, the interplay between quantum theory and general relativity, and higher-order quantum computing. A prominent offshoot of this development is the emergence of indefinite causal order as a feasible resource for quantum information processing. This review provides an overview of the current state of the art in the field, covering the methodology underlying indefinite quantum causality within the so-called "process matrix formalism", outlining key results and experimental implementations, and discussing recent advances.

2. arXiv e-prints

   Entanglement in quantum channel discrimination: sometimes less is more

   K. S. Lien, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   Entanglement is known to be a powerful resource that improves performance in various quantum information and computational tasks. A standard example of such a phenomenon is the possibility of perfectly discriminating all four Pauli operations in a single shot via the superdense coding protocol. While entanglement is often a powerful resource for quantum channel discrimination, this is not necessarily the case. In this work, we identify scenarios in which the maximally entangled state is a bad choice of input state and, more generally, show that excessive entanglement can reduce channel discriminability dramatically. To do so, we present an explicit pair of unitary channels which are perfectly discriminable without entanglement, but for which any strategy with maximally entangled input states is ε-close to a blind uniform guessing strategy. To develop a systematic approach, we introduce the concepts of Maximal Entanglement Worst Case (MEWC) and Maximal Entanglement Best Case (MEBC) pairs of channels, and present conditions for a pair of channels to be MEWC or MEBC. With these conditions, we show that the optimal input states for discriminating MEWC pairs of channels are necessarily separable, and provide non-trivial examples of measurement channels for which entanglement necessarily reduces the maximum probability of discrimination.

3. arXiv e-prints

   The most discriminable quantum states in the multicopy regime

   M. Kvashchuk, P. Chernyshova, L. E. A. Porto, T.-A. Ohst, L. B. Vieira, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   This work investigates which sets of quantum states give rise to the highest achievable success probability in minimum-error state discrimination if multiple copies of the unknown state are given. Specifically, we consider uniformly distributed ensembles of N states in dimension d, each provided in k identical copies, and derive universal limits in this scenario. For pure state ensembles, we prove that whenever N is large enough to support a state k-design, these designs will exactly give rise to the maximally discriminable sets. We further show that when N exceeds the size required for a k-design, mixed states can outperform all pure state ensembles. We then recognise that the problem of most discriminable classical states in the multi-copy regime is in one-to-one correspondence to the concept of the multiplicative Bayes capacity of independent uses of classical channels, a concept that emerges naturally in the context of classical information leakage. This connection allows us to completely solve the classical analogue of our problem when N is at least the binomial coefficient “d+k−1 choose k”, and to prove that quantum systems offer a quadratic advantage (in number of copies k) over classical ones. Then, we prove that this classical over quantum advantage is strongly reduced when one is restricted to real quantum states; more precisely, when N ≥ k+1, pure real qubits only offer a constant advantage over classical bits. Finally, we introduce computational techniques to find sets of most discriminable ensembles and to obtain rigorous universal upper bounds on the maximal success probability for multi-copy state discrimination in cases that are analytically intractable.

4. arXiv e-prints

   Can every set of incompatible measurements lead to genuine multipartite steering?

   L. E. A. Porto, L. Tendick, D. Cavalcanti, R. Uola, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   Measurement incompatibility and bipartite quantum steering are known to display a strong connection: a set of measurements is incompatible if and only if it can lead to bipartite steering. Despite such a close link between these concepts in bipartite scenarios, little is known in the multipartite setting, where notions of genuine multipartite correlations play major roles. In this work we prove that, as in the bipartite case, incompatibility is also necessary and sufficient for genuine multipartite steering in any multipartite scenario with a single uncharacterised party. Interestingly, genuine multipartite steering can be extracted from any set of incompatible measurements using states which are not SLOCC equivalent, such as GHZ and W states. In contrast, we prove that this result does not hold in scenarios with more than one uncharacterised party, by presenting a set of incompatible measurements that can never lead to genuine multipartite steering in these cases. In order to obtain our main results, we introduce methods tailored for multipartite correlations, paving the way to understanding the role of measurement incompatibility beyond bipartite scenarios.

5. arXiv e-prints

   Optimal pure state cloning and transposition are complementary channels

   V. Brzić, D. Grinko, M. Studziński, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   State cloning and state transposition are fundamental transformations which, despite being desirable, cannot be perfectly realised due to two conceptually distinct constraints of quantum theory: cloning is forbidden by linearity, while transposition is ruled out by complete positivity. In this work, we show that, despite these different constraints, the best physically allowed realisation of both transformations arises from a single physical process described by an isometry, which simultaneously implements their best possible approximations. We first determine the optimal fidelity for transforming N qudits into K copies of their transposition and show that, for pure input states, it is achieved by an estimation strategy, which is the unique optimal strategy under the worst-case fidelity figure of merit. We further prove that the corresponding N → K transposition map is the complementary channel of the optimal universal symmetric N → N+K quantum cloning machine on pure states. We then present an explicit quantum circuit that realises N → K transposition and N → N+K cloning in parallel and analyse its gate efficiency. Finally, we investigate mixed-state N → 1 qudit transposition and determine its maximal performance in terms of white-noise visibility, yielding the structural physical approximation of transposition in the multicopy regime.

6. arXiv e-prints

   Post-measurement states are (very) useful for measurement discrimination

   C. Eid, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   The standard approach to quantum measurement discrimination is to perform the given unknown measurement on a probe state, possibly entangled with an auxiliary system, and make a decision based on the measurement outcome obtained. In this work, we go beyond the standard scenarios by considering not only the classical measurement outcome of a measurement, but also its post-measurement quantum state. More specifically, instead of considering only the positive-operator valued measure (POVM) operators, we consider their associated Lüders instruments. We prove that, when the post-measurement quantum states are available, the task of discriminating two qubit projective measurements is equivalent to discriminating two copies of quantum states associated to each projector pair, extending previous results known for the case where probe states are separable. Then, we proceed by showing that the advantage of considering post-measurement states in measurement discrimination can be large. We formalise this claim by presenting a family of pairs of measurements where the ratio between the discrimination bias of the measurement discrimination task with and without post-measurement states can be arbitrarily large. This shows that, while the post-measurement state was neglected in most of the previous literature, its use can significantly improve the performance of quantum measurement discrimination.

7. arXiv e-prints

   Composable simultaneous purification: when all communication scenarios reduce to spatial correlations

   M. Baroni, D. Leichtle, I. Šupić, D. Markham, M.T. Quintino

   arXiv e-prints , (2026)

   Abs arXiv

   Bell non-locality is a powerful framework to distinguish classical, quantum and post-quantum resources, which relies on non-communicating players. Under which restriction can we have the same separations, if we allow for communication? Non-signalling state assemblages, and the fact that they can always be simultaneously purified, turned out to be the key element to restrict the simplest bipartite communication scenario, the prepare-and-measure, to the standard bipartite Bell scenario. Yet, many distinctive features of quantum theory are genuinely multipartite and cannot be reduced to two-party behaviour. In this work we are interested in extending this simultaneous purification inspired result to all multipartite communication schemes. As a first step, we unify and extend the simultaneous purification result from states to instruments and super-instruments, which are composable structures, and open up the possibility to explore more complex communication scenarios. Our main contribution is to establish that arbitrary compositions of non-signalling assemblages cannot escape the standard spatial quantum Bell correlations set. As a consequence, any interactive quantum realization of correlations outside of this set must involve at least one signalling assemblage of quantum operations, even when the resulting correlations are non-signalling.

8. Quantum

   Measurement incompatibility and quantum steering via linear programming

   L. E. A. Porto, S. Designolle, S. Pokutta, M.T. Quintino

   Quantum 10, 2141 (2026)

   Abs arXiv PDF Journal

   The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP). However, the number of variables and constraints in such a formulation grows exponentially with the number of measurements, rendering it intractable for large measurement sets. In this work, we circumvent this problem by transforming the SDP into a hierarchy of linear programs that compute upper and lower bounds on the incompatibility robustness with a complexity that grows polynomially in the number of measurements. The hierarchy is guaranteed to converge and it can be applied to arbitrary measurements – including non-projective POVMs – in arbitrary dimensions. While convergence becomes impractical in high dimensions, in the case of qubits our method reliably provides accurate upper and lower bounds for the incompatibility robustness of sets with several hundred measurements in a short time using a standard laptop. We also apply our methods to qutrits, obtaining non-trivial upper and lower bounds in scenarios that are otherwise intractable using the standard SDP approach. Finally, we show how our methods can be used to construct local hidden state models for states, or conversely, to certify that a given state exhibits steering; for two-qubit quantum states, our approach is comparable to, and in some cases outperforms, the current best methods.

9. Quantum

   Characterising memory in quantum channel discrimination via constrained separability problems

   T.-A. Ohst, S. Zhang, H. C. Nguyen, M. Plávala, M.T. Quintino

   Quantum 10, 1988 (2026)

   Abs arXiv PDF Journal

   Quantum memories are a crucial precondition in many protocols for processing quantum information. A fundamental problem that illustrates this statement is given by the task of channel discrimination, in which an unknown channel drawn from a known random ensemble should be determined by applying it for a single time. In this paper, we characterise the quality of channel discrimination protocols when the quantum memory, quantified by the auxiliary dimension, is limited. This is achieved by formulating the problem in terms of separable quantum states with additional affine constraints that all of their factors in each separable decomposition obey. We discuss the computation of upper and lower bounds to the solutions of such problems which allow for new insights into the role of memory in channel discrimination. In addition to the single-copy scenario, this methodological insight allows to systematically characterise quantum and classical memories in adaptive channel discrimination protocols. Especially, our methods enabled us to identify channel discrimination scenarios where classical or quantum memory is required, and to identify the hierarchical and non-hierarchical relationships within adaptive channel discrimination protocols.

10. Quantum

    Multicopy quantum state teleportation with application to storage and retrieval of quantum programs

    F. Grosshans, M. Horodecki, M. Murao, T. Młynik, M.T. Quintino, M. Studziński, S. Yoshida

    Quantum 10, 2105 (2026)

    Abs arXiv PDF Journal

    This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of multicopy state teleportation, where Alice has k identical copies of an arbitrary unknown d-dimensional qudit state |ψ⟩ to teleport a single copy of |ψ⟩ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob’s correction. Alice may perform a joint measurement on her half of the entangled state and the k copies of |ψ⟩. We prove that the maximal probability of success for teleporting the exact state |ψ⟩ to Bob is p(d,k)=k/(d(k−1+d)) and present an explicit protocol to attain this performance. Then, by utilising k copies of an arbitrary target state |ψ⟩, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.

11. IEEE Trans. Inf. Theory

    One-to-One Correspondence Between Deterministic Port-Based Teleportation and Unitary Estimation

    S. Yoshida, Y. Koizumi, M. Studziński, M.T. Quintino, M. Murao

    IEEE Trans. Inf. Theory 72, 2358–2377 (2026)

    Abs arXiv PDF Journal

    Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations. We show that the optimal fidelity of deterministic port-based teleportation (dPBT) using N=n+1 ports to teleport a d-dimensional state is equivalent to the optimal fidelity of d-dimensional unitary estimation using n calls of the input unitary operation. From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa. Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the bounds 1−O(d⁴)N⁻² ≤ F ≤ 1−Ω(d⁴)N⁻² for the asymptotic optimal fidelity of port-based teleportation, improving the previously known bounds 1−O(d⁵)N⁻² ≤ F ≤ 1−Ω(d²)N⁻². We also show that the optimal fidelity of unitary estimation for n ≤ d−1 is F=(n+1)/d², and this fidelity is equal to the optimal fidelity of unitary inversion with n ≤ d−1 calls of the input unitary operation even if we allow indefinite causal order among the calls.

2025

1. arXiv e-prints

   Higher-order quantum computing with known input states

   V. Brzić, S. Yoshida, M. Murao, M.T. Quintino

   arXiv e-prints , (2025)

   Abs arXiv

   In higher-order quantum computing (HOQC), one typically considers the universal transformation of unknown quantum operations, treated as blackboxes. It is also implicitly assumed that the resulting operation must act on arbitrary, and thus unknown, input states. In this work, we explore a variant of this framework in which the operation remains unknown, but the input state is fixed and known. We argue that this assumption is well-motivated in certain practical contexts, such as unitary programming, and show that classical knowledge of the input state can significantly enhance performance. We demonstrate that in the SAR protocol, this knowledge leads to an exponential advantage through a repeat-until-success strategy, highlighting the operational power of known-state higher-order transformations. Moreover, this assumption allows us to distinguish between protocols designed for pure, bipartite, and mixed states, which enables us to identify the class of mixed states for which deterministic and exact implementation becomes possible.

2. arXiv e-prints

   Can outcome communication explain Bell nonlocality?

   C. Vieira, C. de Gois, P. Lauand, L. E. A. Porto, S. Designolle, M.T. Quintino

   arXiv e-prints , (2025)

   Abs arXiv

   A central aspect of quantum information is that correlations between spacelike separated observers sharing entangled states cannot be reproduced by local hidden variable (LHV) models, a phenomenon known as Bell nonlocality. If one wishes to explain such correlations by classical means, a natural possibility is to allow communication between the parties. In particular, LHV models augmented with two bits of classical communication can explain the correlations of any two-qubit state. Would this still hold if communication is restricted to measurement outcomes? While in certain scenarios with a finite number of inputs the answer is yes, we prove that if a model must reproduce all projective measurements, then for any qubit-qudit state the answer is no. In fact, a qubit-qudit under projective measurements admits an LHV model with outcome communication if and only if it already admits an LHV model without communication. On the other hand, we also show that when restricted sets of measurements are considered (for instance, when the qubit measurements are in the upper hemisphere of the Bloch ball), outcome communication does offer an advantage. This exemplifies that trivial properties in standard LHV scenarios, such as deterministic measurements and outcome-relabelling, play a crucial role in the outcome communication scenario.

3. arXiv e-prints

   Strict hierarchy between n-wise measurement simulability, compatibility structures, and multi-copy compatibility

   L. Tendick, C. Budroni, M.T. Quintino

   arXiv e-prints , (2025)

   Abs arXiv

   The incompatibility of quantum measurements, i.e. the fact that certain observable quantities cannot be measured jointly, is widely regarded as a distinctive quantum feature with important implications for the foundations and the applications of quantum information theory. While the standard incompatibility of multiple measurements has been the focus of attention since the inception of quantum theory, its generalizations, such as measurement simulability, n-wise incompatibility, and multi-copy incompatibility, have only been proposed recently. Here, we point out that all these generalizations are differing notions of the question of how many measurements are genuinely contained in a measurement device. We then show that all notions differ not only in their operational meaning but also mathematically in the set of measurement assemblages they describe. We then fully resolve the relations between these different generalizations by showing a strict hierarchy between these notions. Hence, we provide a general framework for generalized measurement incompatibility. Finally, we consider the implications our results have for recent works using these different notions.

4. arXiv e-prints

   Higher-Order Quantum Operations

   P. Taranto, S. Milz, M. Murao, M.T. Quintino, K. Modi

   arXiv e-prints , (2025)

   Abs arXiv

   An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. Higher-order quantum operations—quantum operations that transform quantum operations—are fundamental to modern quantum theory, extending beyond basic state preparations, evolutions, and measurements described by the Born rule. These operations naturally emerge in quantum circuit architectures, correlated open dynamics, and investigations of quantum causality, to name but a few fields of application. This Review Article provides both a pedagogical introduction to the framework of higher-order quantum operations and a comprehensive survey of current literature, illustrated through physical examples. We conclude by identifying open problems and future research directions in this rapidly evolving field.

5. Nature Communications

   Simulating the quantum switch with quantum circuits is computationally hard

   J. Bavaresco, H. Kristjánsson, M. Murao, T. Odake, M.T. Quintino, P. Taranto, S. Yoshida

   Nature Communications 16, 10216 (2025)

   Abs arXiv PDF Journal

   Higher-order transformations acting on input quantum channels in an indefinite causal order, such as the quantum switch, cannot be described by quantum circuits using the same number of calls to the input channels. A natural question is whether they can be simulated, i.e., whether their action can be exactly and deterministically reproduced by a quantum circuit with more calls to the input channels. Here, we prove that the quantum switch acting on two n-qubit channels cannot be simulated by any quantum circuit using k calls to one channel and one to the other, if k<2^n. This establishes an exponential separation in quantum query complexity between processes with indefinite causal order and quantum circuits. Moreover, even with one extra call to both input channels, such a simulation remains impossible. We further demonstrate the robustness of this separation by extending the result to probabilistic and approximate simulation scenarios.

6. J. Phys. A

   Certifying measurement incompatibility in prepare-and-measure and Bell scenarios

   S. Egelhaaf, J. Pauwels, M.T. Quintino, R. Uola

   J. Phys. A 58, 095304 (2025)

   Abs arXiv PDF Journal

   We consider the problem of certifying measurement incompatibility in a prepare-and-measure (PM) scenario. We present different families of sets of qubit measurements which are incompatible, but cannot lead to any quantum over classical advantage in PM scenarios. Our examples are obtained via a general theorem which proves a set of qubit dichotomic measurements can have their incompatibility certified in a PM scenario if and only if their incompatibility can be certified in a bipartite Bell scenario where the parties share a maximally entangled state. Our framework naturally suggests a hierarchy of increasingly stronger notions of incompatibility, in which more power is given to the classical simulation by increasing its dimensionality. For qubits, we give an example of measurements whose incompatibility can be certified against trit simulations, which we show is the strongest possible notion for qubits in this framework.

7. Phys. Rev. Lett.

   All Incompatible Measurements on Qubits Lead to Multiparticle Bell Nonlocality

   M. Plávala, O. Gühne, M.T. Quintino

   Phys. Rev. Lett. 134, 200201 (2025)

   Abs arXiv PDF Journal

   Bell nonlocality is a fundamental phenomenon of quantum physics as well as an essential resource for various tasks in quantum information processing. It is known that for the observation of nonlocality the measurements on a quantum system have to be incompatible, but the question which incompatible measurements are useful, remained open. Here we prove that any set of incompatible measurements on qubits leads to a violation of a suitable Bell inequality in a multiparticle scenario, where all parties perform the same set of measurements. Since there exists incompatible measurements on qubits which do not lead to Bell nonlocality for two particles, our results demonstrate a fundamental difference between two-particle and multi-particle nonlocality, pointing at the superactivation of measurement incompatibility as a resource. In addition, our results imply that measurement incompatibility for qubits can always be certified in a device-independent manner.

2024

1. arXiv e-prints

   Experimental quantum randomness enhanced by a quantum network

   E. Polino, L. Villegas-Aguilar, D. Poderini, N. Walk, F. Ghafari, M.T. Quintino, A. Lyasota, S. Rogge, R. Chaves, G. J. Pryde, E. G. Cavalcanti, N. Tischler, S. Slussarenko

   arXiv e-prints , (2024)

   Abs arXiv

   The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be unpredictable. However, it is also highly susceptible to noise. Here, we show that extending the conventional bipartite Bell scenario to hybrid quantum networks – which incorporate both quantum channels and entanglement sources – enhances the robustness of certifiable randomness. Our protocol even enables randomness to be certified from Bell-local states, broadening the range of quantum states useful for this task. Through both theoretical analysis and experimental validation in a photonic network, we demonstrate enhanced performance and improved noise resilience.

2. Nature Communications

   Nonlocality activation in a photonic quantum network

   L. Villegas-Aguilar, E. Polino, F. Ghafari, M. T. Quintino, K. T. Laverick, I. R. Berkman, S. Rogge, L. K. Shalm, N. Tischler, E. G. Cavalcanti, S. Slussarenko, G. J. Pryde

   Nature Communications 15, 3112 (2024)

   Abs arXiv PDF Journal

   Bell nonlocality refers to correlations between two distant, entangled particles that challenge classical notions of local causality. Beyond its foundational significance, nonlocality is crucial for device-independent technologies like quantum key distribution and randomness generation. Nonlocality quickly deteriorates in the presence of noise, and restoring nonlocal correlations requires additional resources. These often come in the form of many instances of the input state and joint measurements, incurring a significant resource overhead. Here, we experimentally demonstrate that single copies of Bell-local states, incapable of violating any standard Bell inequality, can give rise to nonlocality after being embedded into a quantum network of multiple parties. We subject the initial entangled state to a quantum channel that broadcasts part of the state to two independent receivers and certify the nonlocality in the resulting network by violating a tailored Bell-like inequality. We obtain these results without making any assumptions about the prepared states, the quantum channel, or the validity of quantum theory. Our findings have fundamental implications for nonlocality and enable the practical use of nonlocal correlations in real-world applications, even in scenarios dominated by noise.

3. Quantum

   Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory

   P. Taranto, M. T. Quintino, M. Murao, S. Milz

   Quantum 8, 1328 (2024)

   Abs arXiv PDF Journal

   Memory is the fundamental form of temporal complexity: when present but uncontrollable, it manifests as non-Markovian noise; conversely, if controllable, memory can be a powerful resource for information processing. Memory effects arise from/are transmitted via interactions between a system and its environment; as such, they can be either classical or quantum. From a practical standpoint, quantum processes with classical memory promise near-term applicability: they are more powerful than their memoryless counterpart, yet at the same time can be controlled over significant timeframes without being spoiled by decoherence. However, despite practical and foundational value, apart from simple two-time scenarios, the distinction between quantum and classical memory remains unexplored. Here, we analyse multi-time quantum processes with memory mechanisms that transmit only classical information forward in time. Complementing this analysis, we also study two related – but simpler to characterise – sets of processes that could also be considered to have classical memory from a structural perspective, and demonstrate that these lead to remarkably distinct phenomena in the multi-time setting. Subsequently, we systematically stratify the full hierarchy of memory effects in quantum mechanics, many levels of which collapse in the two-time setting, making our results genuinely multi-time phenomena.

4. PRX Quantum

   Higher-Order Process Matrix Tomography of a Passively-Stable Quantum Switch

   M. Antesberger, M.T. Quintino, P. Walther, L. A. Rozema

   PRX Quantum 5, 010325 (2024)

   Abs arXiv PDF Journal

   The field of indefinite causal order (ICO) has seen a recent surge in interest. Much of this research has focused on the quantum SWITCH, wherein multiple parties act in a superposition of different orders in a manner transcending the quantum circuit model. This results in a new resource for quantum protocols, and is exciting for its relation to issues in foundational physics. The quantum SWITCH is also an example of a higher-order quantum operation, in that it not only transforms quantum states, but also other quantum operations. To date, no higher-order quantum operation has been completely experimentally characterized. Indeed, past work on the quantum SWITCH has confirmed its ICO by measuring causal witnesses or demonstrating resource advantages, but the complete process matrix has only been described theoretically. Here, we perform higher-order quantum process tomography. However, doing so requires exponentially many measurements with a scaling worse than standard process tomography. We overcome this challenge by creating a new passively-stable fiber-based quantum SWITCH using active optical elements to deterministically generate and manipulate time-bin encoded qubits. Moreover, our new architecture for the quantum SWITCH can be readily scaled to multiple parties. By reconstructing the process matrix, we estimate its fidelity and tailor different causal witnesses directly for our experiment. To achieve this, we measure a set of tomographically complete settings, that also spans the input operation space. Our tomography protocol allows for the characterization and debugging of higher-order quantum operations with and without an ICO, while our experimental time-bin techniques could enable the creation of a new realm of higher-order quantum operations with an ICO.

5. Quantum

   Characterising transformations between quantum objects, ’completeness’ of quantum properties, and transformations without a fixed causal order

   S. Milz, M.T. Quintino

   Quantum 8, 1415 (2024)

   Abs arXiv PDF Journal

   Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels and channels with memory, and also higher-order operations such as superchannels, quantum combs, n-time processes, testers, and process matrices which may not respect a definite causal order. Deducing and characterising their structural properties in terms of linear and semidefinite constraints is not only of foundational relevance, but plays an important role in enabling the numerical optimisation over sets of quantum objects and allowing simpler connections between different concepts and objects. Here, we provide a general framework to deduce these properties in a direct and easy to use way. While primarily guided by practical quantum mechanical considerations, we also extend our analysis to mappings between general linear/affine spaces and derive their properties, opening the possibility for analysing sets which are not explicitly forbidden by quantum theory, but are still not much explored. Together, these results yield versatile and readily applicable tools for all tasks that require the characterisation of linear transformations, in quantum mechanics and beyond. As an application of our methods, we discuss how the existence of indefinite causality naturally emerges in higher-order quantum transformations and provide a simple strategy for the characterisation of mappings that have to preserve properties in a ’complete’ sense, i.e., when acting non-trivially only on parts of an input space.

6. Phys. Rev. Research

   Experimental superposition of a quantum evolution with its time reverse

   T. Strömberg, P. Schiansky, M.T. Quintino, M. Antesberger, L. A. Rozema, I. Agresti, Č. Brukner, P. Walther

   Phys. Rev. Research 6, 023071 (2024)

   Abs arXiv PDF Journal

   In the macroscopic world, time is intrinsically asymmetric, flowing in a specific direction, from past to future. However, the same is not necessarily true for quantum systems, as some quantum processes produce valid quantum evolutions under time reversal. Supposing that such processes can be probed in both time directions, we can also consider quantum processes probed in a coherent superposition of forwards and backwards time directions. This yields a broader class of quantum processes than the ones considered so far in the literature, including those with indefinite causal order. In this work, we demonstrate for the first time an operation belonging to this new class: the quantum time flip. Using a photonic realisation of this operation, we apply it to a game formulated as a discrimination task between two sets of operators. This game not only serves as a witness of an indefinite time direction, but also allows for a computational advantage over strategies using a fixed time direction, and even those with an indefinite causal order.

2023

1. arXiv e-prints

   Possible consequences for physics of the negative resolution of Tsirelson’s problem

   A. Cabello, M.T. Quintino, M. Kleinmann

   arXiv e-prints , (2023)

   Abs arXiv

   In 2020, Ji et al. [arXiv:2001.04383 and Commun. ACM 64, 131 (2021)] proved that the complexity classes MIP* and RE are equivalent. This implies a negative resolution of Tsirelson’s problem: C_qa (the closure of the set of tensor-product correlations) and C_qc (the set of commuting correlations) can be separated by a hyperplane, i.e., a Bell-like inequality. In particular, there are correlations produced by finitely many commuting measurements with finitely many outcomes on an infinite-dimensional quantum system that cannot be approximated by sequences of finite-dimensional tensor-product correlations. We point out four logical possibilities arising from this result, each of which challenges the nature of spatially separated systems in a different way. We list open problems aimed at determining which possibility is correct.

2. Phys. Rev. Lett.

   Demonstration of a quantum SWITCH in a Sagnac configuration

   T. Strömberg, P. Schiansky, R.W. Peterson, M.T. Quintino, P. Walther

   Phys. Rev. Lett. 131, 060803 (2023)

   Abs arXiv PDF Journal

   The quantum SWITCH is an example of a process with an indefinite causal structure, and has attracted attention for its ability to outperform causally ordered computations within the quantum circuit model. To date, realisations of the quantum SWITCH have relied on optical interferometers susceptible to minute path length fluctuations, complicating their design, limiting their performance and posing an obstacle to extending the quantum SWITCH to multiple parties. In this Letter we overcome these limitations by demonstrating an intrinsically stable quantum SWITCH utilizing a common-path geometry facilitated by a novel reciprocal and universal SU(2) polarization gadget. We certify our design by successfully performing a channel discrimination task with near unity success probability.

3. Quantum

   The minimal communication cost for simulating entangled qubits

   M.J. Renner, M.T. Quintino

   Quantum 7, 1149 (2023)

   Abs arXiv PDF Journal

   We analyse the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits. We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by communicating one classical trit. Additionally, when [2p(1−p)/(2p−1)] log[p/(1−p)] + 2(1−p) ≤ 1, approximately 0.835 ≤ p ≤ 1, we present a classical protocol that requires only a single bit of communication. The latter model even allows a perfect classical simulation with an average communication cost that approaches zero in the limit where the degree of entanglement approaches zero (p → 1). This proves that the communication cost for simulating weakly entangled qubit pairs is strictly smaller than for the maximally entangled one.

4. Phys. Rev. Lett.

   Classical cost of transmitting a qubit

   M.J. Renner, A. Tavakoli, M.T. Quintino

   Phys. Rev. Lett. 130, 120801 (2023)

   Abs arXiv PDF Journal

   We consider general prepare-and-measure scenarios in which Alice can transmit qubit states to Bob, who can perform general measurements in the form of positive operator-valued measures (POVMs). We show that the statistics obtained in any such quantum protocol can be simulated by the purely classical means of shared randomness and two bits of communication. Furthermore, we prove that two bits of communication is the minimal cost of a perfect classical simulation. In addition, we apply our methods to Bell scenarios, which extends the well-known Toner and Bacon protocol. In particular, two bits of communication are enough to simulate all quantum correlations associated to arbitrary local POVMs applied to any entangled two-qubit state.

5. IEEE Trans. Inf. Theory

   Optimal Universal Quantum Circuits for Unitary Complex Conjugation

   D. Ebler, M. Horodecki, M. Marciniak, T. Młynik, M.T. Quintino, M. Studziński

   IEEE Trans. Inf. Theory 69, 5069–5082 (2023)

   Abs arXiv PDF Journal

   Let Ud be a unitary operator representing an arbitrary d-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number k of calls of Ud into its complex conjugate Ud¯. Our circuits admit a parallel implementation and are proven to be optimal for any k and d with an average fidelity of ⟨F⟩=(k+1)/(d(d−k)). Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call (k=1) of the operation Ud, and the special case of k=d−1 calls. We then show that our results encompass optimal transformations from k calls of Ud to f(Ud) for any arbitrary homomorphism f from the group of d-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphism on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.

6. SciPost Phys. Core

   Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios

   E.-C. Boghiu, F. Hirsch, P.-S. Lin, M.T. Quintino, J. Bowles

   SciPost Phys. Core 6, 028 (2023)

   Abs arXiv PDF Journal

   It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent entanglement certification. In this work we strengthen these results and explore new aspects of this phenomenon. First, we prove new results related to the activation of Bell nonlocality. We construct Bell inequalities tailored to the broadcast scenario, and show how broadcasting can lead to even stronger notions of Bell nonlocality activation. In particular, we exploit these ideas to show that bipartite states admitting a local hidden-variable model for general measurements can lead to genuine tripartite nonlocal correlations. We then study device-independent entanglement certification in the broadcast scenario, and show through semidefinite programming techniques that device-independent entanglement certification is possible for the two-qubit Werner state in essentially the entire range of entanglement. Finally, we extend the concept of EPR steering to the broadcast scenario, and present novel examples of activation of the two-qubit isotropic state. Our results pave the way for broadcast-based device-dependent and semi-device-independent protocols.

7. Quantum

   The quantum switch is uniquely defined by its action on unitary operations

   Q. Dong, M.T. Quintino, A. Soeda, M. Murao

   Quantum 7, 1169 (2023)

   Abs arXiv PDF Journal

   The quantum switch is a physical process that creates a coherent control between different unitary operations which is often described as a process which transforms a pair of unitary operations (U1,U2) into a controlled unitary operation that coherently applies them in different orders as |0⟩⟨0|⊗U1U2+|1⟩⟨1|⊗U2U1. This description, however, does not directly define its action on non-unitary operations. The action of the quantum switch on non-unitary operations is then chosen to be a "natural" extension of its action on unitary operations. Since, in general, the action of a process on non-unitary operations is not uniquely determined by its action on only unitary operations, in principle, there could be a set of inequivalent extensions of the quantum switch for non-unitary operations. In this paper, we prove that there is a unique way to extend the action of the quantum switch to non-unitary operations. In other words, contrary to the general case, the action of the quantum switch on non-unitary operations is completely determined by its action on unitary operations. We also discuss the general problem of when the complete description of a quantum process is uniquely determined by its action on unitary operations and identify a set of single-slot processes which are completely defined by their action on unitary operations.

2022

1. Quantum

   Deterministic transformations between unitary operations:
   Exponential advantage with adaptive quantum circuits and the power of indefinite causality

   M.T. Quintino, D. Ebler

   Quantum 6, 679 (2022)

   Abs arXiv PDF Journal

   This work analyses the performance of quantum circuits and general processes to transform k uses of an arbitrary unitary operation U into another unitary operation f(U). When the desired function f is a homomorphism, i.e., f(UV)=f(U)f(V), it is known that optimal average fidelity is attainable by parallel circuits and indefinite causality does not provide any advantage. Here we show that the situation changes dramatically when considering anti-homomorphisms, i.e., f(UV)=f(V)f(U). In particular, we prove that when f is an anti-homomorphism, sequential circuits could exponentially outperform parallel ones and processes with indefinite causal order could outperform sequential ones. We present explicit constructions on how to obtain such advantages for the unitary inversion task f(U)=U⁻¹ and the unitary transposition task f(U)=Uᵀ. We also establish a one-to-one connection between the problem of unitary estimation and parallel unitary transposition, allowing one to easily translate results from one field to the other. Finally, we apply our results to several concrete problem instances and present a method based on computer-assisted proofs to show optimality.

2. PRX Quantum

   Quantifying quantumness of channels without entanglement

   H.-Y. Ku, J. Kadlec, A. Černoch, M.T. Quintino, W. Zhou, K. Lemr, N. Lambert, A. Miranowicz, S.-L. Chen, F. Nori, Y.-N. Chen

   PRX Quantum 3, 020338 (2022)

   Abs arXiv PDF Journal

   Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum-information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism, i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum nonbreaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results. (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and nonmacrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of nonbreaking channels using temporal quantum correlations.

3. J. Math. Phys.

   Unitary channel discrimination beyond group structures:
   Advantages of sequential and indefinite-causal-order strategies

   J. Bavaresco, M. Murao, M.T. Quintino

   J. Math. Phys. 63, 042203 (2022)

   Abs arXiv PDF Journal

   For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform parallel ones. Additionally, we show that general strategies that involve indefinite causal order are also advantageous for this task. However, for the task of discriminating a uniformly distributed set of unitary channels that forms a group, we show that parallel strategies are indeed optimal, even when compared to general strategies. We also show that strategies based on the quantum switch cannot outperform sequential strategies in the discrimination of unitary channels. Finally, we derive an ultimate upper bound for the maximal probability of successfully discriminating any set of unitary channels with any number of copies, for the most general strategies that are suitable for channel discrimination. Our bound is tight since it is saturated by sets of unitary channels forming a group k-design.

2021

1. Quantum

   Certifying dimension of quantum systems by sequential projective measurements

   A. Sohbi, D. Markham, J. Kim, M.T. Quintino

   Quantum 5, 472 (2021)

   Abs arXiv PDF Journal

   This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some d. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability.

2. Quantum

   Simple and maximally robust processes with no classical common-cause or direct-cause explanation

   M. Nery, M.T. Quintino, P. A. Guérin, T. O. Maciel, R. O. Vianna

   Quantum 5, 538 (2021)

   Abs arXiv PDF Journal

   Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding whether a process is a direct-cause process is not equivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

3. Phys. Rev. Lett.

   Strict Hierarchy between Parallel, Sequential, and Indefinite-Causal-Order Strategies for Channel Discrimination

   J. Bavaresco, M. Murao, M.T. Quintino

   Phys. Rev. Lett. 127, 200504 (2021)

   Abs arXiv PDF Journal

   We present an instance of a task of minimum-error discrimination of two qubit-qubit quantum channels for which a sequential strategy outperforms any parallel strategy. We then establish two new classes of strategies for channel discrimination that involve indefinite causal order and show that there exists a strict hierarchy among the performance of all four strategies. Our proof technique employs a general method of computer-assisted proofs. We also provide a systematic method for finding pairs of channels that showcase this phenomenon, demonstrating that the hierarchy between the strategies is not exclusive to our main example.

4. Phys. Rev. Lett.

   Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation

   Q. Dong, M.T. Quintino, A. Soeda, M. Murao

   Phys. Rev. Lett. 126, 150504 (2021)

   Abs arXiv PDF Journal

   Repeat-until-success strategy is a standard method to obtain success with a probability which grows exponentially in the number of iterations. However, since quantum systems are disturbed after a quantum measurement, it is not straightforward how to perform repeat-until-success strategies in certain quantum algorithms. In this paper, we propose a new structure for probabilistic higher-order transformation named success-or-draw, which allows a repeat-until-success implementation. For that we provide a universal construction of success-or-draw structure which works for any probabilistic higher-order transformation on unitary operations. We then present a semidefinite programming approach to obtain optimal success-or-draw protocols and analyze in detail the problem of inverting a general unitary operation.

5. Quantum

   Consequences of preserving reversibility in quantum superchannels

   W. Yokojima, M.T. Quintino, A. Soeda, M. Murao

   Quantum 5, 441 (2021)

   Abs arXiv PDF Journal

   Similarly to quantum states, quantum operations can also be transformed by means of quantum superchannels, also known as process matrices. Quantum superchannels with multiple slots are deterministic transformations which take independent quantum operations as inputs. While they are enforced to respect the laws of quantum mechanics, the use of input operations may lack a definite causal order, and characterizations of general superchannels in terms of quantum objects with a physical implementation have been missing. In this paper, we provide a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superchannels preserving the reversibility of quantum operations. We show that the reversibility preserving condition restricts all pure superchannels with two slots to be either a quantum circuit only consisting of unitary operations or a coherent superposition of two unitary quantum circuits where the two input operations are differently ordered. The latter may be seen as a generalization of the quantum switch, allowing a physical interpretation for pure two-slot superchannels. An immediate corollary is that purifiable bipartite processes cannot violate device-independent causal inequalities.

6. Quantum Views

   Quantum teleportation beyond its standard form: Multi-Port-Based Teleportation

   M. T. Quintino

   Quantum Views 5, 56 (2021)

   Journal

2020

1. Quantum

   Bell nonlocality with a single shot

   M. Araújo, F. Hirsch, M.T. Quintino

   Quantum 4, 353 (2020)

   Abs arXiv PDF Journal

   In order to reject the local hidden variables hypothesis, the usefulness of a Bell inequality can be quantified by how small a p-value it will give for a physical experiment. Here we show that to obtain a small expected p-value it is sufficient to have a large gap between the local and Tsirelson bounds of the Bell inequality, when it is formulated as a nonlocal game. We develop an algorithm for transforming an arbitrary Bell inequality into an equivalent nonlocal game with the largest possible gap, and show its results for the CGLMP and Inn22 inequalities. We present explicit examples of Bell inequalities with gap arbitrarily close to one, and show that this makes it possible to reject local hidden variables with arbitrarily small p-value in a single shot, without needing to collect statistics. We also develop an algorithm for calculating local bounds of general Bell inequalities which is significantly faster than the naïve approach, which may be of independent interest.

2019

1. Phys. Rev. A

   Probabilistic exact universal quantum circuits for transforming unitary operations

   M.T. Quintino, Q. Dong, A. Shimbo, A. Soeda, M. Murao

   Phys. Rev. A 100, 062339 (2019)

   Abs arXiv PDF Journal

   This paper addresses the problem of designing universal quantum circuits to transform k uses of a d-dimensional unitary input operation into a unitary output operation in a probabilistic heralded manner. Three classes of protocols are considered: parallel circuits, where the input operations can be used simultaneously; adaptive circuits, where sequential uses of the input operations are allowed; and general protocols, where the input operations may be used without a definite causal order. For these three classes, we develop a systematic semidefinite programming approach that finds a circuit which obtains the desired transformation with the maximal success probability. We then analyse in detail three particular transformations: unitary transposition, unitary complex conjugation, and unitary inversion. For unitary transposition and unitary inversion, we prove that for any fixed dimension d, adaptive circuits have an exponential improvement in terms of uses k when compared to parallel ones. For unitary complex conjugation and unitary inversion, we prove that if the number of uses k is strictly smaller than d−1, the probability of success is necessarily zero. We also discuss the advantage of indefinite causal order protocols over causal ones and introduce the concept of delayed input-state quantum circuits.

2. Phys. Rev. Lett.

   Reversing Unknown Quantum Transformations: Universal Quantum Circuit for Inverting General Unitary Operations

   M.T. Quintino, Q. Dong, A. Shimbo, A. Soeda, M. Murao

   Phys. Rev. Lett. 123, 210502 (2019)

   Abs arXiv PDF Journal

   Given a quantum gate implementing a d-dimensional unitary operation Ud, without any specific description but d, and permitted to use k times, we present a universal probabilistic heralded quantum circuit that implements the exact inverse, whose failure probability decays, exponentially in k. The protocol employs an adaptive strategy, proven necessary for the exponential performance. It requires k≥d−1, proven necessary for exact implementation of U^(−1)_d with quantum circuits. Moreover, even when quantum circuits with indefinite causal order are allowed, k≥d−1 uses are required. We then present a finite set of linear and positive semidefinite constraints characterizing universal unitary inversion protocols and formulate a convex optimization problem whose solution is the maximum success probability for given k and d. The optimal values are computed using semidefinite programming solvers for k≤3 when d=2 and k≤2 for d=3. With this numerical approach we show for the first time that indefinite causal order circuits provide an advantage over causally ordered ones in a task involving multiple uses of the same unitary operation.

3. Phys. Rev. Lett.

   Device-Independent Tests of Structures of Measurement Incompatibility

   M.T. Quintino, C. Budroni, E. Woodhead, A. Cabello, D. Cavalcanti

   Phys. Rev. Lett. 123, 180401 (2019)

   Abs arXiv PDF Journal

   In contrast with classical physics, in quantum physics some sets of measurements are incompatible in the sense that they can not be performed simultaneously. Among other applications, incompatibility allows for contextuality and Bell nonlocality. This makes of crucial importance developing tools for certifying whether a set of measurements posses a certain structure of incompatibility. Here we show that, for quantum or nonsignaling models, if the measurements employed in a Bell test satisfy a given type of compatibility, then the amount of violation of some specific Bell inequalities become limited. Then, we show that correlations arising from local measurements on two-qubit states violate these limits, which rules out in a device-independent way such structures of incompatibility. In particular, we prove that quantum correlations allow for a device-independent demonstration of genuine triplewise incompatibility. Finally, we translate these results into a semi-device-independent Einstein-Podolsky-Rosen-steering scenario.

4. Phys. Rev. A

   Distributed sampling, quantum communication witnesses, and measurement incompatibility

   L. Guerini, M.T. Quintino, L. Aolita

   Phys. Rev. A 100, 042308 (2019)

   Abs arXiv PDF Journal

   We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully-untrusted measurement device. A distributed-sampling task naturally arises in such scenario, whose goal is for Alice and Bob to reproduce the statistics of his measurements on her quantum inputs using a fixed communication channel. Their performance at such task can certify quantum communication (QC), and this is formalised by measurement-device-independent QC witnesses. Furthermore, we prove that QC can provide an advantage (over classical communication) for distributed sampling if and only if Bob’s measurements are incompatible. This gives an operational interpretation to the fundamental notion of measurement incompatibility, and motivates a generalised notion of it. Our findings have both fundamental and applied implications.

5. Quantum

   Semi-device-independent certification of indefinite causal order

   J. Bavaresco, M. Araújo, Č. Brukner, M.T. Quintino

   Quantum 3, 176 (2019)

   Abs arXiv PDF Journal

   When transforming pairs of independent quantum operations according to the fundamental rules of quantum theory, an intriguing phenomenon emerges: some such higher-order operations may act on the input operations in an indefinite causal order. Recently, the formalism of process matrices has been developed to investigate these noncausal properties of higher-order operations. This formalism predicts, in principle, statistics that ensure indefinite causal order even in a device-independent scenario, where the involved operations are not characterised. Nevertheless, all physical implementations of process matrices proposed so far require full characterisation of the involved operations in order to certify such phenomena. Here we consider a semi-device-independent scenario, which does not require all operations to be characterised. We introduce a framework for certifying noncausal properties of process matrices in this intermediate regime and use it to analyse the quantum switch, a well-known higher-order operation, to show that, although it can only lead to causal statistics in a device-independent scenario, it can exhibit noncausal properties in semi-device-independent scenarios. This proves that the quantum switch generates stronger noncausal correlations than it was previously known.

6. Phys. Rev. A

   Implementing positive maps with multiple copies of an input state

   Q. Dong, M.T. Quintino, A. Soeda, M. Murao

   Phys. Rev. A 99, 052352 (2019)

   Abs arXiv PDF Journal

   Valid transformations between quantum states are necessarily described by completely positive maps, instead of just positive maps. Positive but not completely positive maps such as the transposition map cannot be implemented due to the existence of entanglement in composite quantum systems, but there are classes of states for which the positivity is guaranteed, e.g., states not correlated to other systems. In this paper, we introduce the concept of N-copy extension of maps to quantitatively analyze the difference between positive maps and completely positive maps. We consider implementations of the action of positive but not completely positive maps on uncorrelated states by allowing an extra resource of consuming multiple copies of the input state and characterize the positive maps in terms of implementability with multiple copies. We show that by consuming multiple copies, the set of implementable positive maps becomes larger, and almost all positive maps are implementable with finite copies of an input state. The number of copies of the input state required to implement a positive map quantifies the degree by which a positive map violates complete positivity. We then analyze the optimal N-copy implementability of a noisy version of the transposition map.

2018

1. Phys. Rev. A

   Quantum measurement incompatibility does not imply Bell nonlocality

   F. Hirsch, M.T. Quintino, N. Brunner

   Phys. Rev. A 97, 012129 (2018)

   Abs arXiv PDF Journal

   We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we explicitly present a set of non-jointly-measurable POVMs M_A with the following property. Considering a bipartite Bell test where Alice uses M_A, then for any possible shared entangled state ρ and any set of (possibly infinitely many) POVMs M_B performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general.

2017

1. Phys. Rev. A

   Most incompatible measurements for robust steering tests

   J. Bavaresco, M.T. Quintino, L. Guerini, T. O. Maciel, D. Cavalcanti, M.T. Cunha

   Phys. Rev. A 96, 022110 (2017)

   Abs arXiv PDF Journal

   We address the problem of characterizing the steerability of quantum states under restrictive measurement scenarios, i.e., the problem of determining whether a quantum state can demonstrate steering when subjected to N measurements of k outcomes. We consider the cases of either general positive operator-valued measures (POVMs) or specific kinds of measurements (e.g., projective or symmetric). We propose general methods to calculate lower and upper bounds for the white-noise robustness of a d-dimensional quantum state under different measurement scenarios that are also applicable to the study of the noise robustness of the incompatibility of sets of unknown qudit measurements. We show that some mutually unbiased bases, symmetric informationally complete measurements, and other symmetric choices of measurements are not optimal for steering isotropic states and provide candidates to the most incompatible sets of measurements in each case. Finally, we provide numerical evidence that nonprojective POVMs do not improve over projective ones for this task.

2. Quantum

   Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant K_G(3)

   F. Hirsch, M.T. Quintino, T. Vértesi, M. Navascués, N. Brunner

   Quantum 1, 3 (2017)

   Abs arXiv PDF Journal

   We consider the problem of reproducing the correlations obtained by arbitrary local projective measurements on the two-qubit Werner state ρ = v|ψ⁻⟩⟨ψ⁻| + (1−v)I/4 via a local hidden variable (LHV) model, where |ψ⁻⟩ denotes the singlet state. We show analytically that these correlations are local for v = (999×689/10⁶) cos⁴(π/50) ≃ 0.6829. In turn, as this problem is closely related to a purely mathematical one formulated by Grothendieck, our result implies a new bound on the Grothendieck constant K_G(3) ≤ 1/v ≃ 1.4644. We also present a LHV model for reproducing the statistics of arbitrary POVMs on the Werner state for v ≃ 0.4553. The techniques we develop can be adapted to construct LHV models for other entangled states, as well as bounding other Grothendieck constants.

3. Phys. Rev. A

   Tightness of correlation inequalities with no quantum violation

   R. Ramanathan, M.T. Quintino, A.B. Sainz, G. Murta, R. Augusiak

   Phys. Rev. A 95, 012139 (2017)

   Abs arXiv PDF Journal

   We study the faces of the set of quantum correlations, i.e., the Bell and noncontextuality inequalities without any quantum violation. First, we investigate the question whether every proper (tight) Bell inequality for two parties, other than the trivial ones from positivity, normalization and no-signaling can be violated by quantum correlations, i.e., whether the classical Bell polytope or the smaller correlation polytope share any facets with their respective quantum sets. To do this, we develop a recently derived bound on the quantum value of linear games based on the norms of game matrices to give a simple sufficient condition to identify linear games with no quantum advantage. Additionally we show how this bound can be extended to the general class of unique games, illustrating it for the case of three outcomes. We then show as a main result that the paradigmatic examples of correlation Bell inequalities with no quantum violation, namely the non-local computation games do not constitute tight Bell inequalities, not even for the correlation polytope. We also extend this to an arbitrary prime number of outcomes for a specific class of these games. We then study the faces in the simplest CHSH Bell scenario of binary dichotomic measurements, and identify edges in the set of quantum correlations in this scenario. Finally, we relate the non-contextual polytope of single-party correlation inequalities with the cut polytope CUT(∇G), where G denotes the compatibility graph of observables in the contextuality scenario and ∇G denotes the suspension graph of G. We observe that there exist tight non-contextuality inequalities with no quantum violation, and furthermore that this set of inequalities is beyond those implied by the Consistent Exclusivity principle.

2016

1. Phys. Rev. A

   Superactivation of quantum steering

   M.T. Quintino, N. Brunner, M. Huber

   Phys. Rev. A 94, 062123 (2016)

   Abs arXiv PDF Journal

   We consider Einstein-Podolsky-Rosen steering in the regime where the parties can perform collective measurements on many copies of a given shared entangled state. We derive a simple and efficient condition for guaranteeing that an entangled state is k-copy steerable. In particular, we show that all two-qubit and qubit-qutrit entangled states are k-copy steerable. This allows us to discuss the effect of superactivation of steering, whereby an entangled state that is unsteerable (i.e., admits a local hidden state model) in the one-copy regime becomes k-copy steerable. We provide examples with few copies and low dimensions. Our results give evidence that entanglement and steering could become equivalent in the multi-copy regime.

2. New Journal of Physics

   Entanglement without hidden nonlocality

   F. Hirsch, M.T. Quintino, J. Bowles, T. Vértesi, N. Brunner

   New Journal of Physics 18, 113019 (2016)

   Abs arXiv Journal

   We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.

3. Phys. Rev. Lett.

   Algorithmic Construction of Local Hidden Variable Models for Entangled Quantum States

   F. Hirsch, M.T. Quintino, T. Vértesi, M.F. Pusey, N. Brunner

   Phys. Rev. Lett. 117, 190402 (2016)

   Abs arXiv PDF Journal

   Constructing local hidden variable (LHV) models for entangled quantum states is challenging, as the model should reproduce quantum predictions for all possible local measurements. Here we present a simple method for building LHV models, applicable to general entangled states, which consists in verifying that the statistics resulting from a finite set of measurements is local, a much simpler problem. This leads to a sequence of tests which, in the limit, fully capture the set of quantum states admitting a LHV model. Similar methods are developed for constructing local hidden state models. We illustrate the practical relevance of these methods with several examples, and discuss further applications.

4. Phys. Rev. A

   Incompatible quantum measurements admitting a local-hidden-variable model

   M.T. Quintino, J. Bowles, F. Hirsch, N. Brunner

   Phys. Rev. A 93, 052115 (2016)

   Abs arXiv PDF Journal

   The observation of quantum nonlocality, i.e. quantum correlations violating a Bell inequality, implies the use of incompatible local quantum measurements. Here we consider the converse question. That is, can any set of incompatible measurements be used in order to demonstrate Bell inequality violation? Our main result is to construct a local hidden variable model for an incompatible set of qubit measurements. Specifically, we show that if Alice uses this set of measurements, then for any possible shared entangled state, and any possible dichotomic measurements performed by Bob, the resulting statistics are local. This represents significant progress towards proving that measurement incompatibility does not imply Bell nonlocality in general.

5. Phys. Rev. A

   Sufficient criterion for guaranteeing that a two-qubit state is unsteerable

   J. Bowles, F. Hirsch, M.T. Quintino, N. Brunner

   Phys. Rev. A 93, 022121 (2016)

   Abs arXiv PDF Journal

   Quantum steering can be detected via the violation of steering inequalities, which provide sufficient conditions for the steerability of quantum states. Here we discuss the converse problem, namely ensuring that a state is unsteerable, and hence Bell local. We present a simple criterion, applicable to any two-qubit state, which guarantees that the state admits a local hidden state model for arbitrary projective measurements. We find new classes of unsteerable entangled states, which can thus not violate any steering or Bell inequality. In turn, this leads to sufficient conditions for a state to be only one-way steerable, and provides the simplest possible example of one-way steering. Finally, by exploiting the connection between steering and measurement incompatibility, we give a sufficient criterion for a continuous set of qubit measurements to be jointly measurable.

2015

1. Phys. Rev. A

   Inequivalence of entanglement, steering, and Bell nonlocality for general measurements

   M.T. Quintino, T. Vértesi, D. Cavalcanti, R. Augusiak, M. Demianowicz, A. Acín, N. Brunner

   Phys. Rev. A 92, 032107 (2015)

   Abs arXiv PDF Journal

   Einstein-Podolsky-Rosen steering is a form of inseparability in quantum theory commonly acknowledged to be intermediate between entanglement and Bell nonlocality. However, this statement has so far only been proven for a restricted class of measurements, namely projective measurements. Here we prove that entanglement, one-way steering, two-way steering and nonlocality are genuinely different considering general measurements, i.e. single round positive-operator-valued-measures. Finally, we show that the use of sequences of measurements is relevant for steering tests, as they can be used to reveal "hidden steering".

2. Phys. Rev. Lett.

   Local Hidden Variable Models for Entangled Quantum States Using Finite Shared Randomness

   J. Bowles, F. Hirsch, M.T. Quintino, N. Brunner

   Phys. Rev. Lett. 114, 120401 (2015)

   Abs arXiv PDF Journal

   The statistics of local measurements performed on certain entangled states can be reproduced using a local hidden variable (LHV) model. While all known models make use of an infinite amount of shared randomness—the physical relevance of which is questionable—we show that essentially all entangled states admitting a LHV model can be simulated with finite shared randomness. Our most economical model simulates noisy two-qubit Werner states using only 3.58 bits of shared randomness. We also discuss the case of POVMs, and the simulation of nonlocal states with finite shared randomness and finite communication. Our work represents a first step towards quantifying the cost of LHV models for entangled quantum states.

2014

1. Phys. Rev. Lett.

   Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality

   M.T. Quintino, T. Vértesi, N. Brunner

   Phys. Rev. Lett. 113, 160402 (2014)

   Abs arXiv PDF Journal

   We investigate the relation between the incompatibility of quantum measurements and quantum nonlocality. We show that any set of measurements that is not jointly measurable (i.e. incompatible) can be used for demonstrating EPR steering, a form of quantum nonlocality. This implies that EPR steering and (non) joint measurability can be viewed as equivalent. Moreover, we discuss the connection between Bell nonlocality and joint measurability, and give evidence that both notions are inequivalent. Specifically, we exhibit a set of incompatible quantum measurements and show that it does not violate a large class of Bell inequalities. This suggest the existence of incompatible quantum measurements which are Bell local, similarly to certain entangled states which admit a local hidden variable model.

2. Phys. Rev. Lett.

   One-way Einstein-Podolsky-Rosen Steering

   J. Bowles, T. Vértesi, M.T. Quintino, N. Brunner

   Phys. Rev. Lett. 112, 200402 (2014)

   Abs arXiv PDF Journal

   Einstein-Podolsky-Rosen steering is a form of quantum nonlocality exhibiting an inherent asymmetry between the observers, Alice and Bob. We present a simple class of entangled two-qubit states which are one-way steerable, considering arbitrary projective measurements. That is, Alice can steer the state of Bob, but it is impossible for Bob to steer Alice’s state. This shows that the nonlocal properties of entangled states can be fundamentally asymmetrical.

3. Phys. Rev. Lett.

   Certifying the Dimension of Classical and Quantum Systems in a Prepare-and-Measure Scenario with Independent Devices

   J. Bowles, M.T. Quintino, N. Brunner

   Phys. Rev. Lett. 112, 140407 (2014)

   Abs arXiv PDF Journal

   We consider the problem of testing the dimension of uncharacterised classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem non-convex. We present a simple method for generating nonlinear dimension witnesses for systems of arbitrary dimension. The simplest of our witnesses is highly robust to technical imperfections, and can certify the use of qubits in the presence of arbitrary noise and arbitrarily low detection efficiency. Finally, we show that this witness can be used to certify the presence of randomness, suggesting applications in quantum information processing.

2013

1. Phys. Rev. Lett.

   Genuine Hidden Quantum Nonlocality

   F. Hirsch, M.T. Quintino, J. Bowles, N. Brunner

   Phys. Rev. Lett. 111, 160402 (2013)

   Abs arXiv PDF Journal

   The nonlocality of certain quantum states can be revealed by using local filters before performing a standard Bell test. This phenomenon, known as hidden nonlocality, has been so far demonstrated only for a restricted class of measurements, namely projective measurements. Here we prove the existence of genuine hidden nonlocality. Specifically, we present a class of two-qubit entangled states, for which we construct a local model for the most general local measurements (POVMs), and show that the states violate a Bell inequality after local filtering. Hence there exist entangled states, the nonlocality of which can be revealed only by using a sequence of measurements. Finally, we show that genuine hidden nonlocality can be maximal. There exist entangled states for which a sequence of measurements can lead to maximal violation of a Bell inequality, while the statistics of non-sequential measurements is always local.

2. Phys. Rev. A

   All noncontextuality inequalities for the n-cycle scenario

   M. Araújo, M.T. Quintino, C. Budroni, M.T. Cunha, A. Cabello

   Phys. Rev. A 88, 022118 (2013)

   Abs arXiv PDF Journal

   The problem of separating classical from quantum correlations is in general intractable and has been solved explicitly only in few cases. In particular, known methods cannot provide general solutions for an arbitrary number of settings. We provide the complete characterization of the classical correlations and the corresponding maximal quantum violations for the case of n >= 4 observables X_0, ...,X_n-1, where each consecutive pair X_i,X_i+1, sum modulo n, is jointly measurable. This generalizes both the Clauser-Horne-Shimony-Holt and the Klyachko-Can-Binicioglu-Shumovsky scenarios, which are the simplest ones for, respectively, locality and noncontextuality. In addition, we provide explicit quantum states and settings with maximal quantum violation and minimal quantum dimension.

3. Nature Communications

   Realistic loophole-free Bell test with atom–photon entanglement

   C. Teo, M. Araújo, M.T. Quintino, J. Minář, D. Cavalcanti, V. Scarani, M. Terra Cunha, M. França Santos

   Nature Communications 4, 2104 (2013)

   Abs arXiv Journal

   The establishment of nonlocal correlations, obtained through the violation of a Bell inequality, is not only important from a fundamental point of view, but constitutes the basis for device-independent quantum information technologies. Although several nonlocality tests have been performed so far, all of them suffered from either the locality or the detection loopholes. Recent studies have suggested that the use of atom-photon entanglement can lead to Bell inequality violations with moderate transmission and detection efficiencies. In this paper we propose an experimental setup realizing a simple atom-photon entangled state that, under realistic experimental parameters available to date, achieves a significant violation of the Clauser-Horn-Shimony-Holt inequality. Most importantly, the violation remains when considering typical detection efficiencies and losses due to required propagation distances.

2012

1. Phys. Rev. A

   Tests of Bell inequality with arbitrarily low photodetection efficiency and homodyne measurements

   M. Araújo, M.T. Quintino, D. Cavalcanti, M. F. Santos, A. Cabello, M.T. Cunha

   Phys. Rev. A 86, 030101(R) (2012)

   Abs arXiv PDF Journal

   We show that hybrid local measurements combining homodyne measurements and photodetection provide violations of a Bell inequality with arbitrarily low photodetection efficiency. This is shown in two different scenarios: when one part receives an atom entangled to the field mode to be measured by the other part and when both parts make similar photonic measurements. Our findings promote the hybrid measurement scenario as a candidate for loophole-free Bell tests beyond previous expectations.

2. J. Phys. A

   Maximal violations and efficiency requirements for Bell tests with photodetection and homodyne measurements

   M.T. Quintino, M. Araújo, D. Cavalcanti, M.F. Santos, M.T. Cunha

   J. Phys. A 45, 215308 (2012)

   Abs arXiv Journal

   We study nonlocality tests in which each party performs photodetection and homodyne measurements. The results of such measurements are dichotomized and a Clauser-Horne-Shimony-Holt (CHSH) inequality is used. We prove that in this scenario the maximal violation is attainable and fully characterize the set of maximally violating states. If we restrict our search to states composed by at most 2, 4, and 6 photons per mode, we find critical photodetection efficiencies of 0.48, 0.36, and 0.29. We also found an entangled variation of the famous cat states that has critical efficiency 0.32. These values are well within the limit of current photodetector technology, which suggests the present approach as a road for a loophole-free Bell experiment.