Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations

Abstract

What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalisation of Dvoretzky's theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

arXiv comment5 pages, 1 figure v2: more details in the proof of the main result

References in corpus (14)

• Separability of Mixed States: Necessary and Sufficient Conditions
• No Signalling and Quantum Key Distribution
• Quantum Theory From Five Reasonable Axioms
• Probabilistic theories with purification
• Aspects of generic entanglement
• A derivation of quantum theory from physical requirements
• A generalized no-broadcasting theorem
• Most quantum states are too entangled to be useful as computational resources
• A glance beyond the quantum model
• Local Quantum Measurement and No-Signaling Imply Quantum Correlations
• Are random pure states useful for quantum computation?
• Unified Framework for Correlations in Terms of Local Quantum Observables
• Hastings' additivity counterexample via Dvoretzky's theorem
• Experimental undecidability of macroscopic quantumness

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• Semi-device-independent information processing with spatiotemporal degrees of freedom
• Characterization of the probabilistic models that can be embedded in quantum theory
• Intermediate determinism in general probabilistic theories