publications

2023

1. 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.

2. 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 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 automorphisms on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.

3. 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.

4. 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, Bowles J.

   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.

5. arXiv e-prints

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

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

   arXiv e-prints , (2023)

   Abs arXiv

   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 in nature. 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. We first analyse various physically-motivated candidates regarding a suitable definition for classical memory that lead to remarkably distinct phenomena in the multi-time setting. Subsequently, we systematically characterise the hierarchy of multi-time memory effects in quantum mechanics, many levels of which collapse in the two-time setting, thereby making our results genuinely multi-time phenomena.

6. arXiv e-prints

   Logical possibilities for physics after MIP*=RE

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

   arXiv e-prints , (2023)

   Abs arXiv

   MIP*=RE implies that 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) and that there are correlations produced by commuting measurements (a finite number of them and with a finite number of outcomes) on an infinite-dimensional quantum system which cannot be approximated by sequences of finite-dimensional tensor product correlations. We point out that there are four logically possible universes after this result. Each possibility is interesting because it reveals either limitations in accepted physical theories or opportunities to test crucial aspects of nature. We list some open problems that may help us to design a road map to learn in which of these universes we are.

7. arXiv e-prints

   Higher-order Process Matrix Tomography of a passively-stable Quantum SWITCH

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

   arXiv e-prints , (2023)

   Abs arXiv

   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.

8. arXiv e-prints

   Transformations between arbitrary (quantum) objects and the emergence of indefinite causality

   S. Milz, M.T. Quintino

   arXiv e-prints , (2023)

   Abs arXiv 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 optimization 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. Additionally, while primarily guided by practical quantum mechanical considerations, we extend our analysis to mappings between \textitgeneral 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 characterization of linear transformations, in quantum mechanics and beyond. As an application of our methods, we discuss the emergence of indefinite causality in higher-order quantum transformation.

2022

1. 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.

2. arXiv e-prints

   Experimental superposition of time directions

   T. Strömberg, P. Schiansky, M.T. Quintino, M. Antesberger, L. Rozema, T. Agresti, C. Brukner, P. Walther

   arXiv e-prints , (2022)

   Abs arXiv

   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.

3. arXiv e-prints

   The minimal communication cost for simulating entangled qubits

   M.J. Renner, M.T. Quintino

   arXiv e-prints , (2022)

   Abs arXiv

   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−1log(p1−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. 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 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 presented 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 stablish 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.

5. PRX Quantum

   Detecting quantum non-breaking channels without entanglement

   H.-Y. Ku, J. Kadlec, A. Cernoch, 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.

2021

1. 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.

2. 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.

3. 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.

4. 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 weather a process is 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.

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 whichtake 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. arXiv e-prints

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

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

   arXiv e-prints quant-ph, 2106.00034 (2021)

   Abs arXiv

   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 quantum switch on non-unitary operations is then chosen to be a "natural" extension of its action on unitary operation. 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 quantum switch for non-unitary operations. In this paper, we prove that there is a unique way to extend the actions of quantum switch to non-unitary operations. In other words, contrary to the general case, the action of 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.

7. 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 simultaneously, adaptive circuits, where sequential uses of the input-operations are allowed, and general protocols, where the use of the input-operations may be performed 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 inverse, 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 present explicitly a given a set of non jointly measurable POVMs MA with the following property. Considering a bipartite Bell test where Alice uses MA, then for any possible shared entangled state ρ and any set of (possibly infinitely many) POVMs MB 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)14 via a local hidden variable (LHV) model, where |ψ−> denotes the singlet state. We show analytically that these correlations are local for v=999×689×10−6 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 KG(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

   Super-Activation of Quantum Steering

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

   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 any two-qubit and qubit-qutrit entangled states is k-copy steerable. This allows us to discuss the effect of super-activation 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 (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.