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Generalized Householder Transformations
1Institute for Theoretical Physics, TU Wien, Wiedner Hauptstrasse 8-10/136, 1040 Vienna, Austria.
Entropy (Basel, Switzerland)
|March 25, 2022
Summary
This study generalizes the Householder transformation for quantum probabilities. It introduces new operator-valued arguments for contextuality by modifying spectral properties and functional relations.
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.
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