On Exchangeable Continuous Variable Systems

TL;DR

This paper characterizes permutation-invariant continuous variable quantum states and their covariance matrices, establishing criteria and de Finetti-type theorems, especially for Gaussian states, to understand their structure and properties.

Contribution

It provides a complete characterization of permutation-invariant continuous variable states and develops necessary and sufficient criteria, including de Finetti-type theorems for Gaussian states.

Findings

Complete characterization of permutation-invariant states

Necessary and sufficient criteria for Gaussian states

De Finetti-type theorems for various distance measures

Abstract

We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex combinations of tensor power states. On the level of the respective density operators this leads to necessary criteria for all these properties which become necessary and sufficient for Gaussian states. For these we use the derived results to provide de Finetti-type theorems for various distance measures.