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Combinatorics and quantum nonlocality.

Harry Buhrman1, Peter Høyer, Serge Massar

  • 1CWI and University of Amsterdam, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.

Physical Review Letters
|August 9, 2003
PubMed
Summary
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Reproducing quantum correlations with classical theories requires significant communication or high detector efficiency. This study shows these requirements increase with the number of parties involved in quantum experiments.

Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics
  • Quantum Computing

Background:

  • Quantum correlations, as observed in Einstein-Podolsky-Rosen (EPR) and Greenberger-Horne-Zeilinger (GHZ) experiments, challenge classical intuitions.
  • Local hidden-variable (LHV) theories attempt to explain these correlations classically but face limitations.

Purpose of the Study:

  • To derive necessary conditions for reproducing quantum correlations using LHV theories.
  • To quantify the classical communication and detector efficiency needed for such reproduction.
  • To analyze these conditions for multi-party GHZ states.

Main Methods:

  • Utilizing techniques for establishing lower bounds on communication complexity.
  • Applying these bounds to derive constraints on detector efficiency and superluminal communication.

Related Experiment Videos

  • Analyzing the specific case of n-party GHZ states.

    • Main Results:

    • Derived necessary conditions linking detector efficiency and superluminal communication to the possibility of reproducing quantum correlations with LHV theories.
    • Quantified the minimum superluminal classical communication required for n-party GHZ states as at least n(log((2)n-3) bits.
    • Established an upper bound for maximum detector efficiency (eta(*)) as eta(*) <= 8/n, showing it decreases with n.

    Conclusions:

    • Reproducing quantum correlations with LHV theories is fundamentally limited by communication and detector efficiency.
    • These limitations become more stringent as the number of parties (n) in the system increases.
    • The findings provide crucial insights into the boundary between quantum and classical physics.