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Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
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Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities
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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 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.
Forward citations
Cited by 5 Pith papers
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Battery-Explicit Thermodynamic Witnesses of Bell Post-Quantumness
A single excitation is routed by an energy-preserving SWAP into a binary battery whose mean charge equals Δ times (½ + S/8), turning Tsirelson's bound into a quantum ceiling on battery work.
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Battery-Explicit Thermodynamic Witnesses of Bell Post-Quantumness
Constructs a battery-explicit thermodynamic witness that converts Bell-game success probabilities into ceilings on mean battery charge, with Tsirelson's bound as the quantum limit for CHSH.
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Battery-Explicit Thermodynamic Witnesses of Bell Post-Quantumness
Mean battery charge equals Bell game success probability times battery gap, turning local, quantum, and nonsignaling game values into thermodynamic ceilings for XOR games.
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Thermodynamic Value of XOR-Game-Induced Side Information in a Szilard Engine
XOR-game winning probabilities fix the mutual information and thus the reversible Szilard work extractable from game-induced side information, yielding local, quantum and nonsignalling thermodynamic ceilings.
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Thermodynamic Value of XOR-Game-Induced Side Information in a Szilard Engine
CHSH correlations induce a binary-symmetric side-information channel whose mutual information sets the reversible work extractable in a Szilard engine, with quantum and nonsignalling resources outperforming classical ones.
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