Operational Interpretation of the Ratio of Total Correlations to Classical Correlations

TL;DR

This paper explores how non-classical correlations tighten entropic uncertainties in a multi-player measurement game, providing an operational interpretation of the ratio of total to classical correlations and illustrating quantum advantage.

Contribution

It introduces a game-based framework to interpret the ratio of total to classical correlations, linking quantum correlations to operational advantages.

Findings

Maximum number of players with tightened uncertainties identified

Operational interpretation of the correlation ratio established

Quantum advantage demonstrated in the measurement game

Abstract

We will discuss the generalization of entropic uncertainty principles in terms of a game. The game involves k-players, each measuring one of k possible observables. The question is, what is the maximum number of players that can play such that their joint entropic uncertainties are tightened by the presence of non-classical correlations? We answer this question and relate it to the ratio of quantum mutual information to classical correlations. This game hence serves to construct an operational interpretation of the aforementioned ratio. It provides another example of quantum correlations providing a quantum advantage.