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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Graph-theoretic approach to quantum correlations.

Adán Cabello1, Simone Severini2, Andreas Winter3

  • 1Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain.

Physical Review Letters
|March 4, 2014
PubMed
Summary
This summary is machine-generated.

This study connects correlations in Bell inequalities to graph theory. Researchers found that classical, quantum, and general correlations correspond to specific graph numbers, offering a new way to identify quantum correlations.

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Area of Science:

  • Quantum Information Theory
  • Foundations of Physics
  • Combinatorial Optimization

Background:

  • Correlations in Bell and noncontextuality inequalities are key to understanding quantum mechanics.
  • These correlations can be framed as linear combinations of event probabilities.
  • Exclusive events in these correlations can be mapped to graph structures.

Purpose of the Study:

  • To establish a direct link between correlation inequalities and graph theory concepts.
  • To identify combinatorial numbers that characterize classical, quantum, and general correlations.
  • To develop a method for identifying experiments exhibiting quantum correlations.

Main Methods:

  • Representing exclusive events as adjacent graph vertices.
  • Associating correlations with subgraphs.
  • Calculating the independence number, Lovász number, and fractional packing number for these subgraphs.
  • Demonstrating the equivalence between quantum probabilities and the Grötschel-Lovász-Schrijver theta body for specific experiments.

Main Results:

  • The maximum correlation values for classical, quantum, and general theories correspond to the independence number, Lovász number, and fractional packing number of the associated subgraph, respectively.
  • For any graph, a correlation experiment can be constructed where the set of quantum probabilities precisely matches the Grötschel-Lovász-Schrijver theta body.
  • Combinatorial notions are identified as fundamental physical objects in correlation studies.

Conclusions:

  • This work provides a powerful combinatorial framework for analyzing correlations in physics.
  • The findings offer a method to design experiments that specifically probe quantum correlations.
  • The study highlights the deep connection between abstract mathematical concepts and physical reality.