Spatially dependent decoherence and anomalous diffussion of quantum walks

TL;DR

This paper investigates how spatially dependent decoherence affects the long-term behavior of quantum walks, revealing non-Markovian dynamics and sub-ballistic spreading that preserve some quantum features.

Contribution

It demonstrates that spatially dependent decoherence leads to non-Markovian, sub-ballistic quantum walk behavior, challenging previous assumptions about decoherence effects.

Findings

Quantum walks exhibit sub-ballistic behavior under spatially dependent decoherence.

Asymptotic behavior depends on the decoherence strength, showing non-Markovian features.

Long-time Generalized Chiral Distribution reveals the influence of decoherence.

Abstract

We analyze the long time behavior of a discrete time quantum walk subject to decoherence with a strong spatial dependence, acting on one half of the lattice. We show that, except for limiting cases on the decoherence parameter, the quantum walk at late times behaves sub-ballistically, meaning that the characteristic features of the quantum walk are not completely spoiled. Contrarily to expectations, the asymptotic behavior is non Markovian, and depends on the amount of decoherence. This feature can be clearly shown on the long time value of the Generalized Chiral Distribution (GCD).