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Bell's theorem for general N-qubit states.

Marek Zukowski1, Caslav Brukner

  • 1Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet Gdański, PL-80-952 Gdańsk, Poland.

Physical Review Letters
|June 13, 2002
PubMed
Summary

Researchers developed a general Bell inequality to test local realism for N particles. They also found a condition for N-qubit mixed states to violate this inequality, generalizing previous work.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics
  • Many-Body Physics

Background:

  • Local realism posits that physical properties are definite and independent of measurement.
  • Bell inequalities are crucial for experimentally testing local realism against quantum mechanics.
  • Previous work focused on specific numbers of particles or qubits.

Purpose of the Study:

  • To establish a universal condition for N-particle correlations to adhere to local realism.
  • To identify a necessary and sufficient condition for N-qubit mixed states to violate a general Bell inequality.
  • To generalize and reformulate the Horodecki criterion for multipartite entanglement.

Main Methods:

  • Derivation of a single, general Bell inequality applicable to N particles.
  • Analysis of correlation functions under arbitrary dichotomic measurements.
  • Development of a condition for N-qubit mixed states to violate the derived inequality.

Main Results:

  • A single general Bell inequality is presented as a necessary and sufficient condition for N-particle local realism.
  • A novel condition is derived for N-qubit mixed states to violate this general Bell inequality.
  • The new condition is shown to be a generalization of the Horodecki family condition for two qubits.

Conclusions:

  • The derived Bell inequality provides a unified framework for testing local realism in N-particle systems.
  • The condition for violating the inequality offers new insights into multipartite entanglement and quantum correlations.
  • This work advances the understanding of the boundary between classical and quantum physics in many-body systems.

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