Transfer-tensor description of memory effects in open-system dynamics and multi-time statistics

TL;DR

This paper introduces a transfer-tensor framework to analyze memory effects and non-Markovianity in open quantum systems, linking correlations, Markovianity, and multi-time measurement statistics with practical case studies.

Contribution

It develops a hierarchy of transfer tensors to characterize memory effects and connects them with quantum Markovianity and measurement-conditioned dynamics.

Findings

Transfer tensors reveal the role of system-environment correlations.

Quantum Markovianity relates to the composition of 1-step transfer tensors.

The formalism distinguishes different types of memory effects in multi-time statistics.

Abstract

The non-Markovianity of an arbitrary open quantum system is analyzed in reference to the multi-time statistics given by its monitoring at discrete times. On the one hand, we exploit the hierarchy of inhomogeneous transfer tensors, which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the transfer-tensor hierarchy and the CP-divisibility property is then investigated, by showing to what extent quantum Markovianity can be linked to a description of the open-system dynamics by means of the composition of 1-step transfer tensors only. On the other hand, we introduce the set of stochastic transfer tensor transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the transfer-tensor formalism accounts for different kinds of memory effects in the multi-time statistics and allows us to compare them on a similar footing with the memory effects present in non-monitored non-Markovian dynamics, as we illustrate on a spin-boson case study.