Tsirelson bounds for generalized CHSH inequalities
نویسنده
چکیده
Quantum 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 √ 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 X1, . . . , Xn and Y1, . . . , Yn with eigenvalues ±1 we have |〈X1Y1〉+ 〈X2Y1〉+ 〈X2Y2〉+ 〈X3Y2〉+ . . .+ 〈XnYn〉 − 〈X1Yn〉| ≤ 2n cos (
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Quantum 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 √ 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...
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