Sub-fidelity as a measure of irreversibility of decoherence

TL;DR

This paper introduces sub-fidelity as a new measure to quantify the irreversibility of decoherence in quantum systems, linking it to the ability to recover coherence through environmental access.

Contribution

It provides an operational interpretation of sub-fidelity and proposes a family of measures for decoherence irreversibility based on environmental degrees of freedom.

Findings

Sub-fidelity quantifies the irreversibility of decoherence.

Steering ability relates to sub-fidelity of environmental states.

Conjecture of a family of measures for decoherence irreversibility.

Abstract

Quantum correlations between two systems can be impaired by the presence of an environment, as it can make systems decohere. We wish to evaluate how much coherence has been irreversibly lost. To do so, we study two qubits which leak correlations into an arbitrarily large environment and we find that our ability to steer one of them to the most coherent set of states possible by acting on the other is given by the sub-fidelity of two conditional states of the environment. Sub-fidelity is a quantity that was already known, but that until now lacked an operational interpretation. Furthermore, we conjecture the existence of a family of measures, of which fidelity and sub-fidelity are the first two, which measure the irreversibility of decoherence as we gain access to more and more degrees of freedom of the enviroment.