Bounding the dimension of bipartite quantum systems

Details Bounding the dimension of bipartite quantum systems Bounding the dimension of bipartite quantum systems

2008-12-09

arxiv.org/abs/0812.1572v2

Phys. Rev. A 79, 042106 (2009)

Physics

Quantum Physics

9 pages, no figures; published version

Scientific paper

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.

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