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Nonlocality for graph states

  • Quantum Information and Quantum Computation
  • Published:
Laser Physics

Abstract

The possibility of preparing two-photon entangled states encoding three or more qubits in each photon leads to the following problem: If n quabits were distributed between two parties, which quantum pure states and qubit distributions would allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell’s theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs and provide all existing proofs up to n = 7 qubits. On the other hand, the possibility of preparing n-photon n-qubit graph states leads to the following problem: If n qubits were distributed between n parties, which would be the optimal Bell inequalities? We show all optimal n-party Bell inequalities for the perfect correlations of any graph state of n < 6 qubits. Optimal means that the ratio between the quantum violation and the bound for local hidden-variable theories is the maximum over all possible combinations of perfect correlations. This implies that the required detection efficiencies for loophole-free Bell tests are minimal.

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Authors and Affiliations

  1. Departamento de Física Aplicada II, Universidad de Sevilla, Sevilla, E-41012, Spain

    A. Cabello & P. Moreno

  2. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21A, Innsbruck, A-6020, Austria

    O. Gühne

  3. Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, Innsbruck, A-6020, Austria

    O. Gühne

  4. Departamento de Física Aplicada III, Universidad de Sevilla, Sevilla, E-41092, Spain

    D. Rodríguez

Authors
  1. A. Cabello
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  2. O. Gühne
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  3. P. Moreno
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  4. D. Rodríguez
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Corresponding author

Correspondence to A. Cabello.

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Original Text © Astro, Ltd., 2008.

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Cabello, A., Gühne, O., Moreno, P. et al. Nonlocality for graph states. Laser Phys. 18, 335–343 (2008). https://doi.org/10.1134/S1054660X08030249

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  • DOI: https://doi.org/10.1134/S1054660X08030249

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