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A Simplified Basis for Bell-Kochen-Specker Theorems.

James D Malley1, Arthur Fine2

  • 1Center for Information Technology, National Institutes of Health, Bethesda, MD 20892, USA.

Physics Letters. A
|September 9, 2014
PubMed
Summary
This summary is machine-generated.

This study simplifies Bell-Kochen-Specker theorems by showing a weaker condition is sufficient for no-go results. It reveals that if any projector in an identity resolution is 1, at most one projector can be 1.

Keywords:
Bell-Kochen-Specker theoremHidden variablesNo-go

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Area of Science:

  • Quantum mechanics
  • Foundations of physics
  • Quantum information theory

Background:

  • Bell-Kochen-Specker theorems establish fundamental limits in quantum mechanics.
  • These theorems rely on specific structural requirements for deterministic hidden variables.

Purpose of the Study:

  • To investigate a reduced set of structural requirements for deterministic hidden variables.
  • To determine if these reduced requirements are sufficient for the no-go results in Bell-Kochen-Specker theorems.

Main Methods:

  • The study focuses on the principle: an observable takes a spectral value x if and only if the spectral projector associated with x takes the value 1.
  • It proves that the 'only if' part of this principle is sufficient for the no-go results.

Main Results:

  • A significant reduction in the structural requirements for deterministic hidden variables is demonstrated.
  • The 'only if' condition alone is sufficient to yield the no-go results.

Conclusions:

  • The findings simplify the understanding of no-go theorems in quantum mechanics.
  • A key structural feature identified is that in any resolution of the identity, if at least one projector is assigned 1, then at most one projector can be 1.