title: 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 non-local than ordinary qubits, we construct a class of two-superqubit entangled states as a non-local 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 and (3) Modified Rogers. In cases (1) and (2), the winning probability reaches the Tsirelson bound [Formula: see text] of standard quantum mechanics. Case (3) crosses Tsirelson's bound withpwin≃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.
authors.affiliation: Department of Theoretical Physics , Blackett Laboratory, Imperial College London , London SW7 2AZ, UK.
authors.forename: L
authors.initials: L
authors.lastname: Borsten
authors.affiliation: School of Computer Science , McGill University , Montreal, Quebec, Canada H3A 2A7.
authors.forename: K
authors.initials: K
authors.lastname: Brádler
authors.affiliation: Department of Theoretical Physics , Blackett Laboratory, Imperial College London , London SW7 2AZ, UK.
authors.forename: M J
authors.initials: MJ
authors.lastname: Duff
keywords: Clauser; Horne; Shimony and Holt; Tsirelson; entanglement; superqubit