arXiv subjects

Jose Alfredo de Leon

Publications and source records attributed to Jose Alfredo de Leon.

5 recordsLinked to original sources

arXiv2026

Advances in the quantum-state texture theory

The recently introduced concept of quantum-state texture (QST) has found applications ranging from the identification of unknown quantum gates to the study of quantum phase transitions and criticality, and has already been experimentally investigated. Here, we advance its resource-theoretic formulation in several directions. Our approach centers on the experimentally accessible grand sum--the sum of all matrix elements of a density operator in a given basis. We clarify several points raised in the recent literature, including the relation between texture distillation and a simple grand-sum-based QST monotone. We completely characterize free operations for a single qubit and study the resulting state-conversion order; classify relevant families of free operations in arbitrary dimensions; derive bounds relating the texture of composite systems to that of their subsystems; and introduce the basis-independent concept of set texture. Together, these results strengthen and broaden the resource theory of QST, providing a foundation for its further development and applications.

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arXiv2026

The Geometry of Transport in Quantum Walks and Parrondo's Paradox

We study Parrondo's paradox -- the phenomenon where combining losing strategies yields a winning one -- in a minimal discrete-time quantum walk. We introduce the transport vector, encoded in the coin's steady state, whose inner product with the initial coin state gives the walker's asymptotic velocity. More generally, the paradox emerges exactly when the transport vector of the combined strategy falls outside the cone spanned by the individual ones -- a geometric criterion valid for any combination of strategies. It explains, for instance, why composing two coin operators within a single step can produce the paradox while simple alternation between them cannot, since alternation keeps the combined vector confined to the cone. The paradoxical set has nonzero measure, and we compute its probability explicitly in representative cases. This casts the paradox as one instance of designing reachable transport in quantum walks.

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arXiv2026

Dynamical irreversibility and local decoherence in quantum many-body chaos

Typical dynamical quantum chaos probes are initial-state dependent (e.g., local observables or purities) and thus may fail to capture typical decoherent behavior one expects of a subsystem. Quantum channels fully capture the reduced dynamics of a subsystem. Here, we investigate the purity of the Choi state of a single spin in a chain, which acts as the state representation of the channel encoding the reduced dynamics. Operationally, we show this quantity functions as an echo protocol, termed the \textit{Choi echo}. It measures the environment's recovery fidelity when subjected to a forward evolution, a completely depolarizing operation on the local subsystem, and a subsequent backward evolution. We investigate the equilibration value of the Choi echo across the integrability-to-chaos transition in three paradigmatic spin-$1/2$ chains. We show that average single-spin decoherence does not uniquely correspond to spectral chaos. Specifically, coherent transport in integrable systems can mimic the mean relaxation of a single spin typically induced by chaotic scrambling, generating false positives for spectral chaos. This work offers a perspective bridging quantum information tools with many-body quantum chaos.

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arXiv2023

Weyl channels for multipartite systems

Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the use of the Weyl operators. The condition for such maps to be valid quantum channels, i.e. complete positivity, is derived in terms of Fourier transform matrices. From these conditions, we find the extreme points of this set of channels and identify an elegant algebraic structure nested within them. In turn, this allows us to expand upon the concept of "component erasing channels" introduced in earlier work by the authors. We show that these channels are completely characterized by elements drawn of finite cyclic groups. An algorithmic construction for such channels is presented and the smallest subsets of erasing channels which generate the whole set are determined.

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arXiv2022

Pauli component erasing quantum channels

Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that preserve or completely erase the components of a multi-qubit system in the basis of Pauli strings, which we call Pauli component erasing maps. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace, from which we derive several properties and complete the characterization. Moreover, we show that the obtained family of channels forms a semigroup and derive its generators. We use this simple structure to determine physical implementations and connect the obtained family of channels with Markovian processes.

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