A correlation measure detecting almost all non-Markovian evolutions

TL;DR

This paper introduces a new correlation measure that can detect nearly all non-Markovian quantum dynamics, surpassing traditional measures like mutual information and entanglement, with a constructive proof and specific initial states.

Contribution

A novel correlation measure is proposed that detects almost all non-Markovian evolutions in quantum systems, extending beyond existing measures.

Findings

Traditional measures fail to detect all non-Markovian dynamics.

The new measure detects almost all non-Markovian evolutions with two ancillary systems.

Detecting states can be separable and arbitrarily close to product states.

Abstract

We investigate the ability of correlation measures to witness non-Markovian open quantum system dynamics. It is shown that the mutual information and any entanglement measure between the system and an ancilla do not witness all non-Markovian dynamics. A correlation measure is introduced, and it is proven that, in an enlarged setting with two ancillary systems, this measure detects almost all non-Markovian dynamics, except possibly a zero-measure set of dynamics that is non-bijective in finite time-intervals. Our proof is constructive and provides different initial states detecting the non-Markovian evolutions. These states are all separable and some are arbitrarily close to a product state.