Quantum Apices: Identifying Limits of Entanglement, Nonlocality, & Contextuality

TL;DR

This paper introduces analytic methods to delineate quantum phenomena from classical and general probabilistic theories, focusing on limits of nonlocality and contextuality, with practical criteria for entanglement and quantum correlations.

Contribution

It presents a novel analytic approach for determining quantum bounds on Bell inequalities and criteria for separability, advancing understanding of quantum nonlocality and contextuality.

Findings

Derived quantum limits for Bell-type inequalities.

Developed practical separability criteria.

Identified quantum distributions compatible with contextuality but not nonlocality.

Abstract

This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Bell-type linear inequalities. In contrast to semidefinite programming approaches, our method allows for the consideration of inequalities with abstract weights, by means of leveraging the Hermiticity of quantum states. Recognizing that classical correlations correspond to measurements made on separable states, we also introduce a practical method for obtaining sufficient separability criteria. We specifically vet the candidacy of driven and undriven superradiance as schema for entanglement generation. We conclude by reviewing current approaches to quantum contextuality, emphasizing the operational distinction between nonlocal and contextual quantum statistics. We utilize our abstractly-weighted linear quantum bounds to explicitly demonstrate a set of conditional probability distributions which are simultaneously compatible with quantum contextuality while being incompatible with quantum nonlocality. It is noted that this novel statistical regime implies an experimentally-testable target for the Consistent Histories theory of quantum gravity.