Hybrid no-signaling-quantum correlations

• URL: http://arxiv.org/abs/2107.06878v2
• Date: Mon, 16 May 2022 13:00:00 GMT
• Title: Hybrid no-signaling-quantum correlations
• Authors: Micha{\l} Banacki, Piotr Mironowicz, Ravishankar Ramanathan and Pawe{\l} Horodecki
• Abstract summary: We introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term $textbfHNSQ$ in the multi-party Bell scenario. Specifically, the set $textbfHNSQ$ is a super-quantum set of correlations derived from no-signaling assemblages. In contrast to the usual no-signaling correlations, the new set allows for simple security of (one-sided)-device-independent applications against super-quantum adversaries.
• Score: 0.2085467441379275
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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