Abstract
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 , 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 and with eigenvalues we have . 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.
- Received 18 November 2005
- Publisher error corrected 28 February 2006
DOI:https://doi.org/10.1103/PhysRevA.73.022110
©2006 American Physical Society
Corrections
28 February 2006