Classical-like behavior in quantum walks with inhomogeneous, time-dependent coin operators

TL;DR

This paper introduces a quantum walk with an inhomogeneous, time-dependent coin operator that mimics classical random walk behavior at all time scales, challenging the notion that decoherence is necessary for classicality.

Contribution

It presents a novel quantum walk model driven by a time-dependent, inhomogeneous coin that reproduces classical behavior without destroying quantum coherence.

Findings

Quantum walk exhibits classical-like statistical properties at all time scales.

High wave function correlation allows reversing measurement outcomes.

Classical behavior achieved without decoherence.

Abstract

Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I show that this is not the only way: I introduce a quantum walk driven by an inhomogeneous, time-dependent coin operator, which mimics the statistical properties of a random walk at all time scales. The quantum particle undergoes unitary evolution and, in fact, the high correlation evidenced by the components of the wave function can be used to revert the outcome of an accidental measurement of its chirality.