A measure of qubit environment entanglement for pure dephasing evolutions

TL;DR

This paper introduces a specialized entanglement measure for qubit-environment interactions during pure dephasing, offering computational simplicity and a clear physical interpretation, especially suited for solid state quantum systems.

Contribution

It presents a new entanglement measure tailored for pure dephasing evolutions that is easy to compute and interprets entanglement in terms of information content in the environment.

Findings

The measure can be calculated directly from the density matrix without minimization.

It does not require full knowledge of the density matrix, only initial states and conditional environmental states.

The measure provides a physical link between environmental information and qubit-environment entanglement.

Abstract

We propose a qubit-environment entanglement measure which is tailored for evolutions that lead to pure dephasing of the qubit, such as are abundant in solid state scenarios. The measure can be calculated directly form the density matrix without minimization of any kind. In fact it does not require the knowledge of the full density matrix, and it is enough to know the initial qubit state and the states of the environment conditional on qubit pointer states. This yields a computational advantage over standard entanglement measures, which becomes large when there are no correlations between environmental components in the conditional environmental states. In contrast to all other measures of mixed state entanglement, the measure has a straightforward physical interpretation directly linking the amount of information about the qubit state which is contained in the environment to the amount of qubit-environmnent entanglement. This allows for a direct extension of the pure state interpretation of entanglement generated during pure dephasing to mixed states, even though pure-state conclusions about qubit decoherence are not transferable.