arXiv subjects

Zoe G. del Toro

Publications and source records attributed to Zoe G. del Toro.

3 recordsLinked to original sources

arXiv2026

Purification enables an unbounded query separation in sequential quantum channel discrimination

Purifications are often used as a convenient mathematical representation of quantum states and channels when constructing protocols for quantum information processing tasks. Although powerful, this perspective can suggest that the purifying degrees of freedom and its correlations with an environment are just a useful change of representation. Here we show how they can instead be exploited as an operational resource in sequential quantum channel discrimination, even when the environmental reference frame is unknown or averaged. In contrast to state discrimination and parallel channel discrimination, for which bare and averaged-purification access are equivalent, sequential access to purified resources exhibits a strict advantage in probability of success. We prove this strict separation via two main results. In the first, we construct a pair of families of qubit-qubit channels with a strict separation in the two-query case, and in the second, we show an example of a pair of qubit-qubit channels whose purifications are perfectly distinguishable with three queries while no finite number of bare (non-purified) queries suffices for perfect discrimination. These separations imply an advantage of sequential over parallel strategies for channel discrimination and establish the impossibility of converting bare channel queries into averaged-purification queries via transformations that allow arbitrary interventions between queries, strengthening previous results.

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arXiv2026

Probabilistic and approximate universal quantum purification machines

We study the task of lifting arbitrary quantum states and channels to purifications and Stinespring dilations, respectively, in both the probabilistic exact and deterministic approximate settings. We formalize this task through a general framework of quantum purification machines that, given a finite number of copies or uses of a black-box input, aim to output a corresponding purification or Stinespring dilation. In the probabilistic exact setting, we show that universality is not necessary to rule out such transformations: the simple requirement that a machine purifies two inputs of different rank with non-zero probability already implies that it cannot be described by a linear positive map. This simple argument captures a fundamental obstruction of quantum theory and recovers the impossibility of universal probabilistic purification from finitely many copies. In the approximate setting, we allow for general machines that are not required, in general, to produce a pure output. Using the minimum average error as our figure of merit, we derive analytical expressions for the performance of several physically motivated strategies as well as a general upper bound on the achievable error, which is tight in a specific regime. Our analysis reveals a trade-off: strategies that produce a pure output - among which we prove the optimal to be a strategy that produces as a fixed output a maximally entangled purification of the fully depolarizing channel - perform optimally between those considered for large environment dimension, while append-environment strategies that generally produce non-pure outputs perform better at small environment dimension.

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arXiv2024

Aharonov-Bohm effect in phase space

The Aharonov-Bohm effect is a genuine quantum effect typically characterized by a measurable phase shift in the wave function for a charged particle that encircles an electromagnetic field located in a region inaccessible to the mentioned particle. However, this definition is not possible in the majority of the phase space descriptions since they are based on quasiprobability distributions. In this work, we characterize for the first time the Aharonov-Bohm effect within two different formalisms of quantum mechanics. One of them is the phase-space formalism relying on the canonical commutation relations and Weyl transform. In this framework, the aim is to obtain a consistent description of the quantum system by means of the quasiprobability Wigner function. The other one is the Segal-Bargmann formalism, which we mathematically describe and connect with quantum mechanics by means of the commutation relations of the creation and annihilation operators. After an introduction of both formalisms, we study the Aharonov-Bohm effect within them for two specific cases: One determined by a non-zero electric potential, and another determined by a non-zero magnetic vector potential. Subsequently, we obtain a more general description of the Aharonov-Bohm effect that encompasses the two previous cases and that we prove to be equivalent to the well-known description of this effect in the usual quantum mechanics formalism in configuration space. Finally, we delve into the Aharonov-Bohm effect, employing a density operator to depict states with positional and momentum uncertainty, showcasing its manifestation through distinctive interference patterns in the temporal evolution of Wigner functions under an electric potential, and emphasizing the intrinsically quantum nature of this phenomenon.

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