Revealing memory effects in phase-covariant quantum master equations

TL;DR

This paper analyzes how different non-Markovianity indicators detect memory effects in phase-covariant quantum systems, providing analytical conditions and insights into the relations between decay rates without explicit solutions.

Contribution

It derives analytical conditions for non-Markovianity detection in phase-covariant quantum master equations, linking indicators to decay rate relations without explicit coefficient forms.

Findings

Derived conditions for non-Markovianity detection.

Relations between decay rates and indicators.

Insights into memory effects in quantum dynamics.

Abstract

We study and compare the sensitivity of multiple non-Markovianity indicators for a qubit subjected to general phase-covariant noise. For each of the indicators, we derive analytical conditions to detect the dynamics as non-Markovian. We present these conditions as relations between the time-dependent decay rates for the general open system dynamics and its commutative and unital subclasses. These relations tell directly if the dynamics is non-Markovian w.r.t.~each indicator, without the need to explicitly derive and specify the analytic form of the time-dependent coefficients. Moreover, with a shift in perspective, we show that if one assumes only the general form of the master equation, measuring the non-Markovianity indicators gives us directly non-trivial information on the relations between the unknown decay rates.