Laser Physics

, Volume 18, Issue 3, pp 335–343 | Cite as

Nonlocality for graph states

Quantum Information and Quantum Computation

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.

PACS numbers

03.65.Ud 03.67.Pp 03.67.-a 42.50.-p 

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Copyright information

© Pleiades Publishing, Ltd. 2008

Authors and Affiliations

  • A. Cabello
    • 1
  • O. Gühne
    • 2
    • 3
  • P. Moreno
    • 1
  • D. Rodríguez
    • 4
  1. 1.Departamento de Física Aplicada IIUniversidad de SevillaSevillaSpain
  2. 2.Institut für Quantenoptik und QuanteninformationÖsterreichische Akademie der WissenschaftenInnsbruckAustria
  3. 3.Institut für Theoretische PhysikUniversität InnsbruckInnsbruckAustria
  4. 4.Departamento de Física Aplicada IIIUniversidad de SevillaSevillaSpain

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