Complete Characterization of Statistical Constraints in Local Realism and Quantum Mechanics via a Unified Geometric Framework

• URL: http://arxiv.org/abs/2503.05523v1
• Date: Fri, 07 Mar 2025 15:45:56 GMT
• Title: Complete Characterization of Statistical Constraints in Local Realism and Quantum Mechanics via a Unified Geometric Framework
• Authors: Ryosuke Nogami, Jaeha Lee,
• Abstract summary: We propose a unified framework for characterizing statistical constraints in both local realism and quantum mechanics.<n>We derive a general inequality that establishes a necessary and sufficient condition for the existence of a quantum state satisfying given correlation constraints.<n>This result strengthens previously known constraints, such as Tsirel'son's inequalities and the Tsirel'son--Landau inequality.
• Score: 0.8024120666398408
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a unified framework for characterizing statistical constraints in both local realism and quantum mechanics. Employing the Fourier transform of distributions provides a geometric perspective on the problem, while quasi-probability distributions enable a parallel treatment of quantum and local realistic cases. In the Clauser--Horne--Shimony--Holt setup, we derive a general inequality that establishes a necessary and sufficient condition for the existence of a quantum state satisfying given correlation constraints for an arbitrarily fixed set of observables. As part of the proof, we introduce a technique that utilizes symmetries to significantly simplify the problem while preserving its generality. This result strengthens previously known constraints, such as Tsirel'son's inequalities and the Tsirel'son--Landau inequality, by explicitly characterizing statistical constraints for each specified set of observables, and it can be directly applied to Bell's original setting.

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