arXiv subjects

Alejandro Contreras Reynoso

Publications and source records attributed to Alejandro Contreras Reynoso.

2 recordsLinked to original sources

arXiv2026

Orientation-dependent Pauli noise in one-dimensional discrete-time quantum walks

Discrete-time quantum walks exhibit ballistic spreading that is highly sensitive to decoherence. We study the long-time dynamics of a one-dimensional discrete-time quantum walk under Pauli noise acting on the coin. Choosing the unitary coin such that its invariant Bloch-sphere axis is orthogonal to the axis fixed by the conditional shift, we identify the distinct effects of noise aligned with either dynamical axis or orthogonal to both. Using a Fourier-space Pauli-superoperator formalism, we derive expressions for the first two position moments and long-time asymptotics for X-, Y-, Z-, and depolarizing noise. All channels induce a crossover from ballistic to diffusive spreading, with a second moment growing linearly at long times. The approach to this regime is channel dependent: it is exponentially fast for X-, Z-, and depolarizing noise, but algebraic, with a leading $t^{-1/2}$ correction, for Y-noise. The position distributions retain distinct finite-noise signatures, including a Gaussian-like profile with a central depression for Y-noise. In the maximal-noise limit, depolarizing, Y-, and Z-noise yield the classical binomial distribution for arbitrary initial coin states, whereas X-noise does so only when the initial state has no component along the noise axis. Thus, the quantum-to-classical transition is governed by the relative alignment of the noise, the coherent walk dynamics, and the initial state.

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arXiv2023

Normal quantum channels and Markovian correlated two-qubit quantum errors

We study general ``normally'' distributed random unitary transformations. These distributions can be defined in terms of a diffusive random walk in the respective group manifold, formally underpinned by the concept of infinite divisibility. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process, which can be generated by a Lindblad master equation. In the single qubit case, we show that it is possible to find different distributions which induce the same quantum channel. In the case of two qubits, the normal quantum channels, i.e. quantum channels induced by normal distributions in ${\rm SU}(2)\otimes{\rm SU}(2)$ provide an appropriate framework for modeling correlated quantum errors. In contrast to correlated Pauli errors, for instance, they conserve their Markovianity, and they lead to very different results in error correcting codes or entanglement distillation. We expect our work to find applications in the tomography and modeling of one- and two-qubit errors in current quantum computer platforms, but also in the distillation of Bell pairs across imperfect communication channels, where it is conceivable that subsequently transmitted qubits are subject to correlated errors.

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