Marco Túlio Quintino

selected publications

1. 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.

2. 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.

3. 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.

4. 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".

5. 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.