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

Journal Article · Wed Feb 15 00:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.73.022110· OSTI ID:20974512

Wehner, Stephanie ^[1]

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1. CWI, Kruislaan 413, 1098 SJ Amsterdam (Netherlands)

Quantum theory imposes a strict limit on the strength of nonlocal correlations. It only allows for a violation of the Clauser, Horne, Shimony, and Holt (CHSH) inequality up to the value 2{radical}(2), known as Tsirelson's bound. In this paper, 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{sub 1},...,X{sub n} and Y{sub 1},...,Y{sub n} with eigenvalues {+-}1 we have |<X{sub 1}Y{sub 1}>+<X{sub 2}Y{sub 1}>+<X{sub 2}Y{sub 2}>+<X{sub 3}Y{sub 2}>+{center_dot}{center_dot}{center_dot}+<X{sub n}Y{sub n}>-<X{sub 1}Y{sub n}>|{<=}2n 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.

• OSTI ID: 20974512
• Journal Information: Physical Review. A, Vol. 73, Issue 2; Other Information: DOI: 10.1103/PhysRevA.73.022110; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BELL THEOREM
BOUNDARY-VALUE PROBLEMS
CORRELATIONS
EIGENFUNCTIONS
EIGENVALUES
QUANTUM ENTANGLEMENT
VIOLATIONS