Hierarchy of efficiently computable and faithful lower bounds to quantum discord

TL;DR

This paper introduces a hierarchy of efficiently computable lower bounds to quantum discord, converging to a measure of quantum correlations, and providing faithful bounds at the initial levels.

Contribution

It combines multiple quantum information theoretical tools to create a hierarchy of bounds that are both computationally efficient and faithful to quantum discord.

Findings

Hierarchy converges to the surprisal of measurement recoverability.

Provides a faithful lower bound to quantum discord at the lowest non-trivial level.

The initial level of the hierarchy acts as a valid discord-like measure.

Abstract

Quantum discord expresses a fundamental non-classicality of correlations more general than quantum entanglement. We combine the no-local-broadcasting theorem, semidefinite-programming characterizations of quantum fidelity and quantum separability, and a recent breakthrough result of Fawzi and Renner about quantum Markov chains to provide a hierarchy of computationally efficient lower bounds to quantum discord. Such a hierarchy converges to the surprisal of measurement recoverability introduced by Seshadreesan and Wilde, and provides a faithful lower bound to quantum discord already at the lowest non-trivial level. Furthermore, the latter constitutes by itself a valid discord-like measure of the quantumness of correlations.