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Coincidence bell inequality for three three-dimensional systems.

A Acín1, J L Chen, N Gisin

  • 1Institut de Ciències Fotòniques, Jordi Girona 29, Edifici Nexus II, 08034 Barcelona, Spain.

Physical Review Letters
|July 13, 2004
PubMed
Summary

We developed a Bell inequality for three-dimensional quantum systems (qutrits). This inequality is violated by entangled qutrits, confirming quantum mechanics predictions and defining local variable model boundaries.

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Area of Science:

  • Quantum Information Theory
  • Quantum Foundations
  • Entanglement

Background:

  • Bell inequalities test local realism against quantum mechanics.
  • Qutrit systems offer richer quantum phenomena than qubits.
  • Entanglement is a key quantum resource.

Purpose of the Study:

  • To construct and analyze a Bell inequality for a qutrit system.
  • To demonstrate violation of this inequality using entangled qutrits.
  • To explore the implications for local variable models.

Main Methods:

  • Construction of a Bell inequality based on coincidence probabilities.
  • Measurement of noncommuting observables on entangled qutrits using a six-port beam splitter.
  • Comparison with numerical simulations.

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Main Results:

  • A novel Bell inequality for qutrit systems was successfully constructed.
  • The inequality is violated for maximally entangled qutrit states.
  • The violation strength aligns with prior numerical findings.
  • The inequality was proven to define facets of the local variable polytope.

Conclusions:

  • Qutrit systems exhibit non-classical correlations beyond qubit systems.
  • The constructed Bell inequality provides a strong test for quantum mechanics in qutrit systems.
  • This work contributes to understanding the boundary between quantum mechanics and local realism.