Canonical decomposition of quantum correlations in the framework of generalized nonsignaling theories

TL;DR

This paper introduces Bell discord and Mermin discord to classify bipartite quantum correlations within nonsignaling theories, providing a 3-decomposition that isolates nonclassicality sources like PR boxes and EPR-steering.

Contribution

It proposes new measures for nonclassicality, divides the nonsignaling polytope into regions, and offers a 3-decomposition framework for bipartite quantum correlations.

Findings

BD and MD quantify nonclassicality arising from quantum states.

The 3-decomposition isolates nonclassicality sources like PR-box and EPR-steering.

Quantum correlations are constrained within a quantum polytope overlapping all NS regions.

Abstract

We introduce the measures, Bell discord (BD) and Mermin discord (MD), to characterize bipartite quantum correlations in the context of nonsignaling (NS) polytopes. These measures divide the full NS polytope into four regions depending on whether BD and/or MD is zero. This division of the NS polytope allows us to obtain a 3-decomposition that any bipartite box with two binary inputs and two binary outputs can be decomposed into Popescu-Rohrlich (PR) box, a maximally local box, and a local box with BD and MD equal to zero. BD and MD quantify two types of nonclassicality of correlations arising from all quantum correlated states which are neither classical-quantum states nor quantum-classical states. BD and MD serve us the semi-device-independent witnesses of nonclassicality of local boxes in that nonzero value of these measures imply incompatible measurements and nonzero quantum discord only when the dimension of the measured states is fixed. The 3-decomposition serves us to isolate the origin of the two types of nonclassicality into a PR-box and a maximally local box which is related to EPR-steering, respectively. We consider a quantum polytope that has an overlap with all the four regions of the full NS polytope to figure out the constraints of quantum correlations.