Tsirelson's bound and supersymmetric entangled states

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 $p_{win}={\cos }^2\pi /8\simeq 0.8536$ of standard quantum mechanics. Case (3) crosses Tsirelson's bound with $p_{win}\simeq 0.9265$. 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.

arXiv commentUpdated to match published version. Minor modifications. References added

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Cited by in corpus (4)

• Graph Theory and Qubit Information Systems of Extremal Black Branes
• Toric Geometry and String Theory Descriptions of Qudit Systems
• Qubits from Adinkra Graph Theory via Colored Toric Geometry
• On superqubits