Non-Markovian dephasing and depolarizing channels

TL;DR

This paper presents a method to construct and analyze non-Markovian qubit channels, identifying non-Markovianity through CP-divisibility breakdown and quantifying it using two different approaches.

Contribution

It introduces a novel way to create non-Markovian channels and compares two methods for quantifying non-Markovianity, addressing singularities in the process.

Findings

Eigenvalues of the Choi matrix crossover at singularities

Rate becomes negative indicating non-Markovianity

Two methods for quantifying non-Markovianity compared

Abstract

We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP-divisibility of the map, i.e., appearance of a not-completely-positive (NCP) intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation, and thus to a momentary non-invertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP-divisibility (Hall et al., PRA 89, 042120, 2014), which doesn't require optimization but requires normalization to handle the singularity, and another method, based on distinguishability (Breuer et al. PRL 103, 210401, 2009), which requires optimization but is insensitive to the singularity.