On the classicality of quantum dephasing processes

TL;DR

This paper investigates when quantum dephasing processes exhibit classical-like multitime statistics, identifying conditions under which classicality emerges, especially highlighting differences between Markovian and non-Markovian dynamics.

Contribution

It characterizes conditions for classical multitime statistics in quantum dephasing, especially linking Markovianity and basis compatibility to classicality.

Findings

Classicality can be achieved in Markovian dephasing with compatible or mutually unbiased bases.

Non-Markovian processes only show classicality with compatible bases.

Distinct behaviors between Markovian and non-Markovian dephasing processes are identified.

Abstract

We analyze the multitime statistics associated with pure dephasing systems repeatedly probed with sharp measurements, and search for measurement protocols whose statistics satisfies the Kolmogorov consistency conditions possibly up to a finite order. We find a rich phenomenology of quantum dephasing processes which can be interpreted in classical terms. In particular, if the underlying dephasing process is Markovian, we find sufficient conditions under which classicality at every order can be found: this can be reached by choosing the dephasing and measurement basis to be fully compatible or fully incompatible, that is, mutually unbiased bases (MUBs). For non-Markovian processes, classicality can only be proven in the fully compatible case, thus revealing a key difference between Markovian and non-Markovian pure dephasing processes.