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Bell inequalities with auxiliary communication.

D Bacon1, B F Toner

  • 1Institute for Quantum Information, California Institute of Technology, Pasadena, CA 91125, USA. dabacon@cs.caltech.edu

Physical Review Letters
|May 7, 2003
PubMed
Summary

Simulating quantum correlations requires minimal classical communication. One bit of information exchange is sufficient to reproduce quantum correlations under specific local realistic theories, even with multiple measurements.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Quantum Mechanics
  • Computational Complexity

Background:

  • Quantum theory exhibits correlations that defy classical explanation, famously demonstrated by Bell inequalities.
  • Understanding the classical resources needed to simulate quantum phenomena is crucial for quantum information science.
  • Local realistic theories provide a framework for comparing classical and quantum correlation capabilities.

Purpose of the Study:

  • To determine the minimum classical communication cost for simulating quantum correlations.
  • To generalize Bell inequalities for local realistic theories with added classical communication.
  • To investigate the sufficiency of one bit of communication for simulating quantum correlations.

Main Methods:

  • Generalization of Bell inequalities to incorporate classical communication.
  • Analysis of M two-outcome measurements with 1 bit of information exchange.
  • Derivation of complete inequality sets for M=2 and joint correlations for M=3.

Main Results:

  • Quantum correlations were found to satisfy the derived sets of inequalities.
  • The study confirms that one bit of classical communication is sufficient to simulate quantum correlations in the considered scenarios.
  • Complete sets of inequalities were established for M=2 and M=3.

Conclusions:

  • Quantum correlations can be simulated within local realistic theories using a surprisingly small amount of classical communication (1 bit).
  • This finding has implications for understanding the boundary between quantum and classical information processing.
  • The generalized Bell inequalities provide a tool for quantifying simulation costs.

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