Non-Markovian random unitary qubit dynamics

TL;DR

This paper compares two approaches to non-Markovian quantum evolution in qubits, highlighting their differences and similarities, and shows that entropy can increase monotonically even in non-Markovian dynamics.

Contribution

It provides a detailed comparison of divisible maps and distinguishability-based approaches, illustrating their differences with a simple qubit example and characterizing both via local decoherence rates.

Findings

The two approaches differ in their characterization of non-Markovianity.

Both approaches can be described using local decoherence rates.

Entropy can increase monotonically even in non-Markovian qubit dynamics.

Abstract

We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates. As a byproduct it is shown that entropy might monotonically increase even for non-Markovian qubit dynamics.