Non-Markovianity and memory of the initial state

TL;DR

This paper investigates the relationship between non-Markovian dynamics and quantum memory performance in open quantum systems, demonstrating that non-Markovianity influences but does not solely determine the system's ability to store information.

Contribution

It provides a rigorous analysis linking non-Markovianity, measured by the BLP measure, to quantum memory fidelity in a two-level system coupled to a bosonic bath.

Findings

Non-Markovianity affects quantum memory performance.

Recovery fidelity is related but not solely determined by non-Markovianity.

Explicit calculations show environment structure impacts results.

Abstract

We explore in a rigorous manner the intuitive connection between the non-Markovianity of the evolution of an open quantum system and the performance of the system as a quantum memory. Using the paradigmatic case of a two-level open quantum system coupled to a bosonic bath, we compute the recovery fidelity, which measures the best possible performance of the system to store a qubit of information. We deduce that this quantity is connected, but not uniquely determined, by the non-Markovianity, for which we adopt the BLP measure proposed in \cite{breuer2009}. We illustrate our findings with explicit calculations for the case of a structured environment.