Finite de Finetti theorem for conditional probability distributions describing physical theories

TL;DR

This paper generalizes the classical finite de Finetti theorem to a broad class of physical theories, including quantum mechanics, showing that symmetric states can be approximated by convex combinations of i.i.d. distributions under no-signalling constraints.

Contribution

It extends the finite de Finetti theorem to general physical theories with no-signalling, applicable to quantum correlations without local dimension bounds.

Findings

Symmetric states can be approximated by convex combinations of i.i.d. distributions.

Results apply to quantum correlations without local dimension restrictions.

Generalizes classical de Finetti theorem to broader physical frameworks.

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.