Complete positivity, finite temperature effects, and additivity of noise for time-local qubit dynamics

TL;DR

This paper develops a comprehensive model for qubit dynamics incorporating thermalization and dephasing effects beyond Markovian assumptions, analyzing complete positivity, temperature effects, and noise additivity in non-Markovian regimes.

Contribution

It introduces a general, physically consistent model for qubit dynamics that captures thermal and dephasing effects beyond Markovian limits, including conditions for complete positivity.

Findings

Noise additivity holds beyond Markovian limit

Temperature influences non-Markovian behavior

Heuristic model ensures physicality and correct Markovian limit

Abstract

We present a general model of qubit dynamics which entails pure dephasing and dissipative time-local master equations. This allows us to describe the combined effect of thermalisation and dephasing beyond the usual Markovian approximation. We investigate the complete positivity conditions and introduce a heuristic model that is always physical and provides the correct Markovian limit. We study the effects of temperature on the non-Markovian behaviour of the system and show that the noise additivity property discussed by Yu and Eberly in Ref. [1] holds beyond the Markovian limit.