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Gisin's theorem for three qubits.

Jing-Ling Chen1, Chunfeng Wu, L C Kwek

  • 1Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542. phycj@nus.edu.sg

Physical Review Letters
|November 5, 2004
PubMed
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All pure entangled states in three-qubit systems violate Bell inequalities for probabilities. This generalizes Gisin's theorem, proving that entanglement in these systems inherently breaks Bell's inequality.

Area of Science:

  • Quantum Information Science
  • Quantum Mechanics
  • Entanglement Theory

Background:

  • Bell inequalities are crucial for understanding quantum mechanics and distinguishing quantum correlations from classical ones.
  • Previous work established Gisin's theorem for two-qubit systems, showing all entangled states violate Bell inequalities.

Purpose of the Study:

  • To investigate whether all pure entangled states of a three-qubit system violate a Bell inequality.
  • To generalize Gisin's theorem to the three-qubit scenario.

Main Methods:

  • The study presents a theorem concerning generalized Greenberger-Horne-Zeilinger (GHZ) states.
  • The analysis focuses on Bell inequalities expressed in terms of probabilities.

Main Results:

Related Experiment Videos

  • A theorem is presented proving that all generalized Greenberger-Horne-Zeilinger states of a three-qubit system violate a Bell inequality in terms of probabilities.
  • It is demonstrated that all pure entangled states of a three-qubit system violate a Bell inequality for probabilities.

Conclusions:

  • The findings establish Gisin's theorem for three-qubit systems.
  • All pure entangled three-qubit states exhibit non-classical correlations that violate Bell inequalities.