Diagonal quantum discord

TL;DR

This paper introduces and analyzes diagonal quantum discord, a simplified, easily computable measure of quantum correlations that retains desirable properties and connects to thermodynamics and resource theory.

Contribution

It demonstrates that diagonal discord is a practical alternative to optimized discord, proving its monotonicity, continuity, and applicability to resource theories for non-degenerate local states.

Findings

Diagonal discord is easily computable.

Diagonal discord is monotonic under certain channels.

Diagonal discord is continuous with a Fannes-like bound.

Abstract

Quantum discord measures quantum correlation by comparing the quantum mutual information with the maximal amount of mutual information accessible to a quantum measurement. This paper analyzes the properties of diagonal discord, a simplified version of discord that compares quantum mutual information with the mutual information revealed by a measurement that correspond to the eigenstates of the local density matrices. In contrast to the optimized discord, diagonal discord is easily computable; it also finds connections to thermodynamics and resource theory. Here we further show that, for the generic case of non-degenerate local density matrices, diagonal discord exhibits desirable properties as a preferable discord measure. We employ the theory of resource destroying maps [Liu/Hu/Lloyd, PRL 118, 060502 (2017)] to prove that diagonal discord is monotonically nonincreasing under the operation of local discord nongenerating qudit channels, $d>2$, and provide numerical evidence that such monotonicity holds for qubit channels as well. We also show that it is continuous, and derive a Fannes-like continuity bound. Our results hold for a variety of simple discord measures generalized from diagonal discord.