Three-particle Bell-like inequalities under Lorentz transformations

Three-particle Bell-like inequalities under Lorentz transformations We study the effects of Lorentz transformations on three-particle nonlocal system states (GHZ and W) of spin 1/2 particles, using the Pauli spin operator and a three-particle generalization of Bell’s inequality, introduced by Svetlichny. In our setup, the moving and laboratory frames used the (same) set of measurement directions that maximally violate Svetlichny’s inequality in the laboratory frame. We also investigate the behavior of Mermin’s and Collins’ inequalities. We find that, regardless of the particles’ type of entanglement, violation of Svetlichny’s inequality in the moving frame is decreased by increasing the boost velocity and the energy of particles in the laboratory frame. In the relativistic regime, Svetlichny’s inequality is a good criterion to investigate the nonlocality of the GHZ state. We also find that Mermin’s and Collins’ inequalities lead to reasonable predictions, in agreement with the behavior of the spin state, about nonlocality of the W state in the relativistic regime. Then, comparing our results with those in which Czachor’s relativistic spin is used instead of the Pauli operator, we find that the results obtained by considering the Pauli spin operator are in better agreement with the behavior of spin state of the system in the relativistic information theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Three-particle Bell-like inequalities under Lorentz transformations

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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1064-3
Publisher site
See Article on Publisher Site

Abstract

We study the effects of Lorentz transformations on three-particle nonlocal system states (GHZ and W) of spin 1/2 particles, using the Pauli spin operator and a three-particle generalization of Bell’s inequality, introduced by Svetlichny. In our setup, the moving and laboratory frames used the (same) set of measurement directions that maximally violate Svetlichny’s inequality in the laboratory frame. We also investigate the behavior of Mermin’s and Collins’ inequalities. We find that, regardless of the particles’ type of entanglement, violation of Svetlichny’s inequality in the moving frame is decreased by increasing the boost velocity and the energy of particles in the laboratory frame. In the relativistic regime, Svetlichny’s inequality is a good criterion to investigate the nonlocality of the GHZ state. We also find that Mermin’s and Collins’ inequalities lead to reasonable predictions, in agreement with the behavior of the spin state, about nonlocality of the W state in the relativistic regime. Then, comparing our results with those in which Czachor’s relativistic spin is used instead of the Pauli operator, we find that the results obtained by considering the Pauli spin operator are in better agreement with the behavior of spin state of the system in the relativistic information theory.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 14, 2015

References

  • Can quantum-mechanical description of physical reality be considered complete?
    Einstein, E; Podolsky, B; Rosen, N
  • On hidden variables and quantum mechanical probabilities
    Wigner, EP

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