A tight Tsirelson inequality for infinitely many outcomes

Details A tight Tsirelson inequality for infinitely many outcomes A tight Tsirelson inequality for infinitely many outcomes

2010-03-02

arxiv.org/abs/1003.0616v2

Europhysics Letters 90 (2010) 10002

Physics

Quantum Physics

5 pages, 2 figures; improved presentation, change in title, as published.

Scientific paper

10.1209/0295-5075/90/10002

We present a novel tight bound on the quantum violations of the CGLMP inequality in the case of infinitely many outcomes. Like in the case of Tsirelson's inequality the proof of our new inequality does not require any assumptions on the dimension of the Hilbert space or kinds of operators involved. However, it is seen that the maximal violation is obtained by the conjectured best measurements and a pure, but not maximally entangled, state. We give an approximate state which, in the limit where the number of outcomes tends to infinity, goes to the optimal state for this setting. This state might be potentially relevant for experimental verifications of Bell inequalities through multi-dimenisonal entangled photon pairs.

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