Quantumness in decoherent quantum walk using measurement-induced disturbance

TL;DR

This paper investigates how quantum correlations, measured by measurement-induced disturbance, reveal the classicalization process in decoherent quantum walks on lines and cycles, showing cyclic walks classicalize faster due to phase randomization.

Contribution

It introduces a measure based on measurement-induced disturbance to quantify classicalization in decoherent quantum walks on different topologies.

Findings

Cyclic quantum walks tend to classicalize faster than linear walks.

Measurement-induced disturbance effectively indicates the degree of quantum correlations.

Noise modeled by SGAD channel influences the rate of classicalization.

Abstract

The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability distribution becomes increasingly Gaussian, with a concomitant fall in the standard deviation, in the former case, but not in the latter. As another example, each step of the quantum walk on a line may be subjected to an arbitrary phase gate, without affecting the position probability distribution, no matter whether the walk is noiseless or noisy. This symmetry, which is absent in the case of noiseless cyclic walk, but is restored in the presence of sufficient noise, serves as an indicator of classicalization, but only in the cyclic case. Here we show that the degree of quantum correlations between the coin and position degrees of freedom, quantified by a measure based on the disturbance induced by local measurements (Luo, Phys. Rev. A 77, 022301 (2008)), provides a suitable measure of classicalization across both type of walks. Applying this measure to compare the two walks, we find that cyclic quantum walks tend to classicalize faster than quantum walks on a line because of more efficient phase randomization due to the self-interference of the two counter-rotating waves. We model noise as acting on the coin, and given by the squeezed generalized amplitude damping (SGAD) channel, which generalizes the generalized amplitude damping channel.