Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities

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dc.creatorWehner, Stephanie
dc.date2005-10-11
dc.date2006-01-14
dc.date.accessioned2026-07-07T06:48:42Z
dc.date.available2026-07-07T06:48:42Z
dc.descriptionQuantum theory imposes a strict limit on the strength of non-local correlations. It only allows for a violation of the CHSH inequality up to the value 2 sqrt(2), known as Tsirelson's bound. In this note, we consider generalized CHSH inequalities based on many measurement settings with two possible measurement outcomes each. We demonstrate how to prove Tsirelson bounds for any such generalized CHSH inequality using semidefinite programming. As an example, we show that for any shared entangled state and observables X_1,...,X_n and Y_1,...,Y_n with eigenvalues +/- 1 we have |<X_1 Y_1> + <X_2 Y_1> + <X_2 Y_2> + <X_3 Y_2> + ... + <X_n Y_n> - <X_1 Y_n>| <= 2 n cos(pi/(2n)). It is well known that there exist observables such that equality can be achieved. However, we show that these are indeed optimal. Our approach can easily be generalized to other inequalities for such observables.
dc.description9 pages, LateX, V2: Updated reference [3]. To appear in Physical Review A
dc.identifierhttps://arxiv.org/abs/quant-ph/0510076
dc.identifierhttp://arxiv.org/abs/quant-ph/0510076
dc.identifierPhys. Rev. A, 73, 022110 (2006)
dc.identifierdoi:10.1103/PhysRevA.73.022110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104105
dc.subjectQuantum Physics
dc.titleTsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
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