A study of Wigner functions for discrete-time quantum walks

TL;DR

This paper investigates the behavior of Wigner functions in one-dimensional discrete-time quantum walks, focusing on negativity and entanglement to understand quantum-classical transition aspects.

Contribution

It introduces a systematic analysis of Wigner functions with chirality in quantum walks, linking negativity to entanglement and system dynamics.

Findings

Negativity in phase space varies with initial states and time.

Negativity correlates with entanglement between coin and walker.

Provides insights into quantum versus classical behavior in quantum walks.

Abstract

We perform a systematic study of the discrete time Quantum Walk on one dimension using Wigner functions, which are generalized to include the chirality (or coin) degree of freedom. In particular, we analyze the evolution of the negative volume in phase space, as a function of time, for different initial states. This negativity can be used to quantify the degree of departure of the system from a classical state. We also relate this quantity to the entanglement between the coin and walker subspaces.