Source-linked AI summary
Hierarchy of efficiently computable and faithful lower bounds to quantum discord
Marco Piani
TL;DR
Standard quantum discord is difficult to compute, and general easily computable lower bounds are not known. This paper uses local broadcasting and semidefinite programming to construct a hierarchy of computable lower bounds that converges to the surprisal of measurement recoverability and is faithful from its lowest non-trivial level.
Problem
Standard quantum discord is difficult to compute even in simple cases, and general easily computable lower bounds are similarly not known.
Source: p. 1Method
The paper uses local broadcasting and semidefinite-programming techniques to construct computable lower bounds to the surprisal of measurement recoverability that converge to it.
Source: p. 2Results
The hierarchy converges to the surprisal of measurement recoverability, and its lowest non-trivial level is strictly positive for every state that is not classical on B.
Source: pp. 2, 4Takeaways & Limitations
Each element of the hierarchy is a valid discord-like quantifier and lower bound to standard quantum discord.
Source: pp. 1, 5
Abstract
from arXiv · showhide
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.