Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord

TL;DR

This paper compares two measures of quantumness, measurement-induced disturbance and quantum discord, in noisy quantum walks, revealing that MID often overestimates non-classicality and can sometimes misrepresent the effects of noise.

Contribution

It provides a comparative analysis of MID and QD in noisy quantum walks, highlighting the limitations and trends of MID as an approximation of quantum discord.

Findings

MID generally bounds QD from above but can overestimate non-classicality.

MID reflects trends in quantum discord behavior under noise.

An instance where MID increases with noise, contrary to expectations.

Abstract

Noisy quantum walks are studied from the perspective of comparing their quantumness as defined by two popular measures, measurement-induced disturbance (MID) and quantum discord (QD). While the former has an operational definition, unlike the latter, it also tends to overestimate non-classicality because of a lack of optimization over local measurements. Applied to quantum walks, we find that MID, while acting as a loose upper bound on QD, still tends to reflect correctly the trends in the behavior of the latter. However, there are regimes where its behavior is not indicative of non-classicality: in particular, we find an instance where MID increases with the application of noise, where we expect a reduction of quantumness.