Non-Markovian quantum processes: complete framework and efficient characterisation

TL;DR

This paper introduces a comprehensive framework for characterizing non-Markovian quantum processes, enabling experimental reconstruction and efficient representation, thus advancing understanding of memory effects in quantum systems.

Contribution

It develops a universal method to describe and reconstruct non-Markovian quantum processes using a many-body quantum state representation with potential for efficient matrix product operator forms.

Findings

Experimental reconstruction of non-Markovian processes is feasible.

Temporal correlations can be mapped to spatial correlations in a quantum state.

The framework provides an effective description of memory effects in open quantum systems.

Abstract

Currently, there is no systematic way to describe a quantum process with memory solely in terms of experimentally accessible quantities. However, recent technological advances mean we have control over systems at scales where memory effects are non-negligible. The lack of such an operational description has hindered advances in understanding physical, chemical and biological processes, where often unjustified theoretical assumptions are made to render a dynamical description tractable. This has led to theories plagued with unphysical results and no consensus on what a quantum Markov (memoryless) process is. Here, we develop a universal framework to characterise arbitrary non-Markovian quantum processes. We show how a multi-time non-Markovian process can be reconstructed experimentally, and that it has a natural representation as a many body quantum state, where temporal correlations are mapped to spatial ones. Moreover, this state is expected to have an efficient matrix product operator form in many cases. Our framework constitutes a systematic tool for the effective description of memory-bearing open-system evolutions.