Two-point measurement correlations beyond the quantum regression theorem

TL;DR

This paper explores the limitations of the quantum regression theorem in non-Markovian open quantum systems, introducing methods to analyze quantum features like entanglement and coherence when the theorem fails.

Contribution

It extends the analysis of temporal correlations beyond the regression theorem, providing tools to uncover quantum features in non-Markovian systems where the theorem does not hold.

Findings

Breakdown of the regression theorem reveals quantum entanglement and coherence.

Methods link quantum features to microscopic properties like bath spectral density.

Quantum memory cannot be simulated by classical feedback in non-Markovian processes.

Abstract

Temporal correlations are fundamental in quantum physics, yet their computation is often challenging. The regression theorem (or hypothesis) serves as a key tool in this context, offering a seemingly straightforward approach. However, it fails for systems strongly coupled to their surroundings, where memory effects become significant. Here, we extend the analysis of temporal correlations beyond the regression theorem, revealing what can be learned about open quantum systems when this hypothesis fails. We introduce robust, operationally meaningful methods to explore how the breakdown of the regression hypothesis can uncover fundamental quantum features of non-Markovian open systems, including entanglement, coherence, and quantum memory, namely, the fundamental impossibility of simulating memory in non-Markov processes with classical feedback mechanisms. Finally, we demonstrate how these quantum features are linked to microscopic properties such as the bath spectral density and heat flow.