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Generalized Householder Transformations.

Karl Svozil1

  • 1Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria.

Entropy (Basel, Switzerland)
|March 25, 2022
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Summary
This summary is machine-generated.

This study generalizes the Householder transformation for quantum probabilities. It introduces new operator-valued arguments for contextuality by modifying spectral properties and functional relations.

Keywords:
Householder transformationaffine transformationexpectation valueprobability distribution

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Area of Science:

  • Quantum mechanics
  • Mathematical physics

Background:

  • The Householder transformation relates probabilities to expectations of dichotomic observables.
  • Understanding quantum contextuality is crucial for foundational studies.

Purpose of the Study:

  • To generalize the Householder transformation using spectral decomposition.
  • To explore new avenues for operator-valued arguments in quantum contextuality.

Main Methods:

  • Spectral decomposition of the Householder transformation.
  • Modulating dichotomy via eigenvalues and non-binary observables.
  • Analyzing functional relations and operator additivity.

Main Results:

  • A generalized Householder transformation is formulated.
  • New operator-valued arguments for contextuality are derived.
  • Contextuality is explored through variations in operator functional relations.

Conclusions:

  • The generalized transformation offers a novel perspective on quantum probabilities.
  • This work extends the understanding of quantum contextuality and its mathematical framework.