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This study resolves the question of whether positive operator-valued measures (POVMs) aid in demonstrating Bell nonlocality. A local hidden state model for Werner states under general POVMs was constructed, closing the Werner gap.

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Area of Science:

  • Quantum information theory
  • Foundations of quantum mechanics

Background:

  • Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are key concepts in quantum mechanics.
  • The role of positive operator-valued measures (POVMs) in demonstrating these phenomena, particularly with noisy quantum states like Werner states, remained an open problem.
  • The 'Werner gap' specifically refers to the range of visibility in Werner states for which nonlocality could not be definitively shown using certain models.

Purpose of the Study:

  • To determine if positive operator-valued measures (POVMs) offer advantages in demonstrating Bell nonlocality.
  • To resolve the long-standing open problem concerning the Werner gap in the context of EPR steering with Werner states.
  • To construct a local hidden state model for Werner states under general POVMs.

Main Methods:

  • Construction of a local hidden state model for Werner states with visibility r≤1/2.
  • Development of an exact measurement compatibility model for noisy POVMs.
  • Application of the model to analyze EPR steering scenarios.

Main Results:

  • A local hidden state model was successfully constructed for Werner states with any visibility r≤1/2 under general POVMs.
  • This construction effectively closes the Werner gap.
  • A local hidden variable model was provided for a broader range of Werner states than previously established.

Conclusions:

  • Positive operator-valued measures (POVMs) do not provide an advantage in demonstrating Bell nonlocality for Werner states within the studied parameter range.
  • The developed measurement compatibility model is crucial for constructing the local hidden state and variable models.
  • This work significantly advances the understanding of nonlocality and hidden variable models in quantum mechanics.