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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
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Tsirelson's bound and supersymmetric entangled states.
L Borsten1, K Brádler2, M J Duff1
1Department of Theoretical Physics , Blackett Laboratory, Imperial College London , London SW7 2AZ, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 9, 2014
Summary
Superqubits, a minimal supersymmetric extension of qubits, were tested for non-locality in the CHSH game. One probability extraction method allowed superqubits to violate Bell
Area of Science:
- Quantum Information Science
- Supersymmetry in Physics
- Quantum Non-locality
Background:
- The conventional qubit is the fundamental unit of quantum information.
- Superqubits extend the qubit concept into supersymmetric quantum mechanics.
- Non-locality is a key feature of quantum mechanics, explored via Bell inequalities.
Purpose of the Study:
- To investigate the non-locality of superqubits compared to conventional qubits.
- To construct and analyze entangled two-superqubit states for the CHSH game.
- To explore different methods for extracting real probabilities from Grassmann-valued super Hilbert space amplitudes.
Main Methods:
- Construction of entangled two-superqubit states.
- Application of these states in the Clauser-Horne-Shimony-Holt (CHSH) game.
- Examination of three distinct probability extraction maps: DeWitt, Trigonometric, and Modified Rogers.
Main Results:
- The DeWitt and Trigonometric maps resulted in winning probabilities reaching the Tsirelson bound.
- The Modified Rogers map enabled superqubits to exceed the Tsirelson bound, with a winning probability of approximately 0.9265.
- The Modified Rogers map also allowed for basis changes that yielded negative transition probabilities.
Conclusions:
- Superqubits, under specific probability extraction methods, can exhibit non-locality beyond classical limits.
- The choice of probability extraction significantly impacts the observed non-locality in superqubit systems.
- The Modified Rogers map reveals novel aspects of superqubit behavior, including potential negative transition probabilities.
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