A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes

TL;DR

This paper extends the transfer-tensor formalism to multi-time measurement scenarios in open quantum systems, enabling efficient computation of multi-time correlations without detailed environment modeling.

Contribution

The authors introduce a generalized transfer-tensor method for multi-time correlations in non-Markovian quantum processes, leveraging the process-tensor framework.

Findings

Successfully applied to the spin-boson model

Computed steady-state emission spectra with correlations

Demonstrated efficient propagation of multi-time correlations

Abstract

Efficient simulations of the dynamics of open systems is of wide importance for quantum science and tech-nology. Here, we introduce a generalization of the transfer-tensor, or discrete-time memory kernel, formalism to multi-time measurement scenarios. The transfer-tensor method sets out to compute the state of an open few-body quantum system at long times, given that only short-time system trajectories are available. Here, we showthat the transfer-tensor method can be extended to processes which include multiple interrogations (e.g. measurements) of the open system dynamics as it evolves, allowing us to propagate high order short-time correlation functions to later times, without further recourse to the underlying system-environment evolution. Our approach exploits the process-tensor description of open quantum processes to represent and propagate the dynamics in terms of an object from which any multi-time correlation can be extracted. As an illustration of the utility of the method, we study the build-up of system-environment correlations in the paradigmatic spin-boson model, and compute steady-state emission spectra, taking fully into account system-environment correlations present in the steady state.