Characterizing non-Markovianity via quantum coherence based on Kirkwood-Dirac quasiprobability

TL;DR

This paper introduces a new measure of non-Markovianity using quantum coherence derived from Kirkwood-Dirac quasiprobability, offering an experimentally accessible and intuitive way to detect memory effects in quantum systems.

Contribution

It proposes a novel non-Markovianity measure based on KD quasiprobability coherence, expanding the tools for analyzing quantum memory effects with practical advantages.

Findings

The measure detects non-Markovianity effectively in dissipation and dephasing dynamics.

It performs at least as well as traditional $ ext{l}_1$-norm coherence measures.

The approach provides a new perspective on non-Markovian quantum dynamics.

Abstract

We present a new measure of non-Markovianity based on the property of nonincreasing quantum coherence via Kirkwood-Dirac (KD) quasiprobability under incoherent completely positive trace-preserving maps. Quantum coherence via the KD quasiprobability is defined as the imaginary part of the KD quasiprobability, which is maximised over all possible second bases and evaluated using an incoherent reference basis. A measure non-Markovianity based on KD quasiprobability coherence would capture memory effects via the time evolution of the imaginary part of the KD quasiprobability, providing an experimentally accessible and physically intuitive alternative to traditional measures relying on quantum Fisher information or trace distance. This approach is applied to the study of dissipation and dephasing dynamics in single- and two-qubit systems. The results obtained show that, in the cases studied, our measure based on coherence via Kirkwood-Dirac quasiprobability performs at least as well as $\ell_{1}$-norm coherence in detecting non-Markovianity, this provides a novel perspective on the analysis of non-Markovian dynamics.