Bipartite polygon models: entanglement classes and their nonlocal behaviour

Abstract

Hardy's argument constitutes an elegantly logical test for identifying nonlocal features of multipartite correlations. In this paper, we investigate Hardy's nonlocal behavior within a broad class of operational theories, including the qubit state space as a specific case. Specifically, we begin by examining a wider range of operational models with state space descriptions in the form of regular polygons. First, we present a systematic method to characterize the possible forms of entangled states within bipartite compositions of these models. Then, through explicit examples, we identify the classes of entangled states that exhibit Hardy-type nonlocality. Remarkably, our findings highlight a closer analogy between odd polygon models and the qubit state space in terms of their bipartite Hardy nonlocal behavior compared to even-sided polygons. Furthermore, we demonstrate that the emergence of mixed-state Hardy nonlocality in any operational model is determined by a specific symmetry inherent in its dynamic description. Finally, our results uncover an unexplored class of almost-quantum correlations that can be associated with an explicit operational model.

22+8 pages (1 column), 7 figures; comments are welcome

References in corpus (36)

• Quantum entanglement
• Bell nonlocality
• Hidden Variables and the Two Theorems of John Bell
• Informational derivation of Quantum Theory
• Quantum Theory From Five Reasonable Axioms
• Probabilistic theories with purification
• Randomness vs Non Locality and Entanglement
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Almost quantum correlations
• All Pure Bipartite Entangled States can be Self-Tested
• Generalized Probability Theories: What determines the structure of quantum theory?
• Limits on non-local correlations from the structure of the local state space
• The structure of reversible computation determines the self-duality of quantum theory
• Device-independent bounds for Hardy's experiment
• No-hypersignaling principle
• Joint measurements of spin, operational locality and uncertainty
• Dimension of physical systems, information processing, and thermodynamics
• Nonlocality Without Entanglement: Quantum Theory and Beyond
• Hardy's nonlocality argument as witness for post-quantum correlation
• Almost quantum correlations violate the no-restriction hypothesis
• Information and communication in polygon theories
• Two-Qubit Pure Entanglement as Optimal Social Welfare Resource in Bayesian Game
• Persistence of nonlocality for bipartite quantum spin systems
• Self-testing quantum states via nonmaximal violation in Hardy's test of nonlocality
• Reversibility and the structure of the local state space
• Device-independent bounds from Cabello's nonlocality argument
• The principle of information symmetry constrains the state-space in any physical theory
• Advantage of Quantum Theory Over Non-classical Models of Communication
• Practical No-Signalling proof Randomness Amplification using Hardy paradoxes and its experimental implementation
• Local Orthogonality provides better upper bound for Hardy's nonlocality
• Classical analogue of quantum superdense coding and communication advantage of a single quantum system
• Teleportation in General Probabilistic Theories
• Local simulation of singlet statistics for restricted set of measurement
• Timelike correlations and quantum tensor product structure
• Maximum tri-partite Hardy's nonlocality respecting all bi-partite principles
• Quantum theory is exclusive: a distributed computing setup