Quantum regression theorem and non-Markovianity of quantum dynamics

TL;DR

This paper investigates the relationship between non-Markovian quantum dynamics and the validity of the quantum regression theorem, revealing that violations can occur in both Markovian and non-Markovian regimes through exact analysis.

Contribution

It provides a detailed comparison between non-Markovianity measures and the quantum regression theorem, including exact evaluations for specific models.

Findings

Non-Markovian dynamics often violate the quantum regression theorem.

Markovian dynamics can also lead to violations of the regression relation.

Exact evaluations reveal nuanced relationships between non-Markovianity and regression hypothesis.

Abstract

We explore the connection between two recently introduced notions of non-Markovian quantum dynamics and the validity of the so-called quantum regression theorem. While non-Markovianity of a quantum dynamics has been defined looking at the behaviour in time of the statistical operator, which determines the evolution of mean values, the quantum regression theorem makes statements about the behaviour of system correlation functions of order two and higher. The comparison relies on an estimate of the validity of the quantum regression hypothesis, which can be obtained exactly evaluating two points correlation functions. To this aim we consider a qubit undergoing dephasing due to interaction with a bosonic bath, comparing the exact evaluation of the non-Markovianity measures with the violation of the quantum regression theorem for a class of spectral densities. We further study a photonic dephasing model, recently exploited for the experimental measurement of non-Markovianity. It appears that while a non-Markovian dynamics according to either definition brings with itself violation of the regression hypothesis, even Markovian dynamics can lead to a failure of the regression relation.