Monday, July 2, 2012

1206.6934 (L. Borsten et al.)

Tsirelson's bound and supersymmetric entangled states    [PDF]

L. Borsten, K. Bradler, M. J. Duff
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 pi/8 \simeq 0.8536 of standard quantum mechanics. Case (3) crosses Tsirelson's bound with p(win) = 0.9265. 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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