Finite de Finetti theorem for conditional probability distributions describing physical theories

Abstract

We work in a general framework where the state of a physical system is defined by its behaviour under measurement and the global state is constrained by no-signalling conditions. We show that the marginals of symmetric states in such theories can be approximated by convex combinations of independent and identical conditional probability distributions, generalizing the classical finite de Finetti theorem of Diaconis and Freedman. Our results apply to correlations obtained from quantum states even when there is no bound on the local dimension, so that known quantum de Finetti theorems cannot be used.

Published version. 10 pages, 1 figure

References in corpus (14)

• Device-independent security of quantum cryptography against collective attacks
• No Signalling and Quantum Key Distribution
• From Bell's Theorem to Secure Quantum Key Distribution
• Unknown Quantum States: The Quantum de Finetti Representation
• Symmetry implies independence
• A generalized no-broadcasting theorem
• Monogamy of nonlocal quantum correlations
• One-and-a-half quantum de Finetti theorems
• Hiding classical data in multi-partite quantum states
• A de Finetti representation for finite symmetric quantum states
• Secrecy extraction from no-signalling correlations
• Local Hidden Variable Theories for Quantum States
• Multiparty data hiding of quantum information
• A de Finetti Representation Theorem for Quantum Process Tomography

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• Limitations on device independent key secure against non signaling adversary via the squashed non-locality
• On Exchangeable Continuous Variable Systems
• Monogamy of entanglement between cones
• Secure One-Sided Device-Independent Quantum Key Distribution Under Collective Attacks with Enhanced Robustness
• De Finetti Theorems for Braided Parafermions
• A de Finetti theorem for quantum causal structures
• De Finetti Theorems for Quantum Conditional Probability Distributions with Symmetry