On random classical marginal problems with applications to quantum information theory
arXiv:2406.14153 · doi:10.1088/1751-8121/adb547
Abstract
In this paper, we study random instances of the classical marginal problem. We encode the problem in a graph, where the vertices have assigned fixed binary probability distributions, and edges have assigned random bivariate distributions having the incident vertex distributions as marginals. We provide estimates on the probability that a joint distribution on the graph exists, having the bivariate edge distributions as marginals. Our study is motivated by Fine's theorem in quantum mechanics. We study in great detail the graphs corresponding to CHSH and Bell-Wigner scenarios providing rations of volumes between the local and non-signaling polytopes.
References in corpus (22)
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Bell nonlocality
- A simple test for hidden variables in spin-1 system
- Graph-Theoretic Approach to Quantum Correlations
- Quantum marginal problem and N-representability
- A Combinatorial Approach to Nonlocality and Contextuality
- All noncontextuality inequalities for the n-cycle scenario
- The contextual fraction as a measure of contextuality
- An entropic approach to local realism and noncontextuality
- All the noncontextuality inequalities for arbitrary prepare-and-measure experiments with respect to any fixed sets of operational equivalences
- Survey on Nonlocal Games and Operator Space Theory
- Concentration phenomena in the geometry of Bell correlations
- Measures of Contextuality and Noncontextuality
- Quantum Correlations in the Minimal Scenario
- How much larger quantum correlations are than classical ones
- Compatibility of subsystem states
- Exponentially many entanglement and correlation constraints for multipartite quantum states
- Inequalities witnessing coherence, nonlocality, and contextuality
- Bell inequalities from variable elimination methods
- The extension problem for partial Boolean structures in Quantum Mechanics
- Random quantum correlations are generically non-classical
- No contextual advantage in non-paradoxical scenarios of two state vector formalism