Bounding the dimension of bipartite quantum systems

TL;DR

This paper proves that infinite-dimensional bipartite quantum systems are necessary to generate all possible joint correlations, and identifies a minimum number of measurements needed to surpass two-dimensional system capabilities.

Contribution

The authors demonstrate that finite-dimensional systems cannot produce all bipartite quantum correlations and establish a lower bound on the number of measurements required.

Findings

No finite dimension suffices for all bipartite correlations.

At least 10 measurements are needed to generate correlations beyond two-dimensional systems.

An explicit example with 11 settings illustrates the minimal case.

Abstract

Let us consider the set of joint quantum correlations arising from two-outcome local measurements on a bipartite quantum system. We prove that no finite dimension is sufficient to generate all these sets. We approach the problem in two different ways by constructing explicit examples for every dimension d, which demonstrates that there exist bipartite correlations that necessitate d-dimensional local quantum systems in order to generate them. We also show that at least 10 two-outcome measurements must be carried out by the two parties altogether so as to generate bipartite joint correlations not achievable by two-dimensional local systems. The smallest explicit example we found involves 11 settings.