de Finetti reductions for correlations

TL;DR

This paper introduces a new de Finetti theorem based on measurement statistics rather than internal quantum states, facilitating analysis of permutation-invariant systems in device-independent quantum protocols.

Contribution

It presents a novel de Finetti theorem that relates measurement statistics to independence, applicable when system dimensions are unknown, unlike traditional theorems.

Findings

Provides a measurement-based de Finetti reduction for correlations.

Enables analysis of device-independent quantum protocols.

Applicable to systems with unknown dimensions.

Abstract

When analysing quantum information processing protocols one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structure. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations.