Unified Framework for Correlations in Terms of Local Quantum Observables

TL;DR

This paper introduces a unified framework for describing multipartite correlations in quantum and classical systems using local measurements and an operator, revealing a gap in correlations for three or more parties.

Contribution

It generalizes Gleason's Theorem to multipartite systems and identifies a fundamental difference in correlations when three or more parties are involved.

Findings

Unified framework for correlations via local measurements and an operator

Extension of Gleason's Theorem to multipartite systems

Existence of a gap in correlations for three or more parties

Abstract

We provide a unified framework for nonsignalling quantum and classical multipartite correlations, allowing all to be written as the trace of some local (quantum) measurements multiplied by an operator. The properties of this operator define the corresponding set of correlations.We then show that if the theory is such that all local quantum measurements are possible, one obtains the correlations corresponding to the extension of Gleason's Theorem to multipartite systems. Such correlations coincide with the quantum ones for one and two parties, but we prove the existence of a gap for three or more parties.