Hybrid no-signaling-quantum correlations

TL;DR

This paper introduces the hybrid no-signaling-quantum set $ extbf{HNSQ}$, a new framework for non-local correlations that combines quantum and no-signaling constraints, with implications for quantum security and optimization.

Contribution

It defines the $ extbf{HNSQ}$ set, develops a semi-definite programming hierarchy for it, and demonstrates its unique properties and potential for quantum security applications.

Findings

Existence of quantum-realizable extreme points in $ extbf{HNSQ}$

Numerical analysis of Bell inequality violations in tripartite scenarios

Potential for simplified security proofs against super-quantum adversaries

Abstract

Fundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term $\textbf{HNSQ}$ in the multi-party Bell scenario where some subsystems are locally quantum while the remaining subsystems are only constrained by the no-signaling principle. Specifically, the set $\textbf{HNSQ}$ is a super-quantum set of correlations derived from no-signaling assemblages by performing quantum measurements on the trusted subsystems. As a tool for optimization over the set $\textbf{HNSQ}$, we introduce an outer hierarchy of semi-definite programming approximations to the set following an approach put forward by Doherty-Parillo-Spedalieri. We then show that in contrast to the set $\textbf{NS}$ of no-signaling correlations, there exist extreme points of $\textbf{HNSQ}$ in the tripartite Bell scenario that admit quantum realization. We perform an extensive numerical analysis of the maximal violation of the facet Bell inequalities in the three-party binary input-output scenario and study the corresponding self-testing properties. In contrast to the usual no-signaling correlations, the new set allows for simple security proofs of (one-sided)-device-independent applications against super-quantum adversaries.