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Area of Science:

  • Quantum Physics
  • Foundations of Quantum Theory
  • Quantum Information Processing

Background:

  • Constructing local hidden variable (LHV) models for entangled quantum states is essential for understanding quantum theory's foundations.
  • Reproducing quantum predictions for all possible local measurements presents a significant challenge in this field.

Purpose of the Study:

  • To present a simple and broadly applicable method for building LHV models for any entangled quantum state.
  • To develop a sequence of tests that, in the limit, fully characterizes quantum states admitting an LHV model.
  • To extend similar methods for local hidden state models and demonstrate practical relevance.

Main Methods:

  • Development of a novel, simple method for constructing LHV models.
  • Inclusion of continuous sets of measurements in the modeling process.
  • Formulation of a limiting sequence of tests to capture all quantum states with LHV models.

Main Results:

  • A general method for building LHV models for entangled quantum states has been established.
  • The method accounts for continuous measurement sets, enhancing its applicability.
  • The developed tests effectively characterize quantum states compatible with LHV models.

Conclusions:

  • The presented method offers a practical approach to constructing LHV models for quantum states.
  • This work advances the understanding of quantum foundations and has implications for quantum information processing.
  • The methods are illustrated with examples, highlighting their practical significance.