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Noisy quantum walks are studied from the perspective of comparing theirquantumness 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 alack of optimization over local measurements. Applied to quantum walks, we findthat MID, while acting as a loose upper bound on QD, still tends to reflectcorrectly the trends in the behavior of the latter. However, there are regimeswhere its behavior is not indicative of non-classicality: in particular, wefind an instance where MID increases with the application of noise, where weexpect a reduction of quantumness.

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