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arXiv · 1206.6934

Tsirelson's bound and supersymmetric entangled states

L. Borsten·K. Bradler·M. J. Duff
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Abstract

A superqubit, belonging to a $(2|1)$-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more nonlocal than ordinary qubits, we construct a class of two-superqubit entangled states as a nonlocal resource in the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the result depends on how we extract real probabilities and we examine three choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1) and (2) the winning probability reaches the Tsirelson bound $p_{win}=\cos^2{π/8}\simeq0.8536$ of standard quantum mechanics. Case (3) crosses Tsirelson's bound with $p_{win}\simeq0.9265$. Although all states used in the game involve probabilities lying between 0 and 1, case (3) permits other changes of basis inducing negative transition probabilities.

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L. Borsten, K. Bradler, M. J. Duff. 2014-09-06. Tsirelson's bound and supersymmetric entangled states. https://doi.org/10.1098/rspa.2014.0253

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