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Open Quantum Systems Decoherence
Comment on "Gleason-Type Theorem for Projective Measurements, Including Qubits" by F. De Zela
arXiv
Authors: Michael J. W. Hall
Year
2016
Paper ID
42613
Status
Preprint
Abstract Read
~2 min
Abstract Words
91
Citations
N/A
Abstract
It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding assumptions related to continuity and the existence of 'eigenstates'. This amounts to a claim of the derivation of Born's rule for Hermitian qubit observables. I point out a simple counterexample, and the flaw in De Zela's derivation (these are equally applicable to the repetition of the derivation given in a recent Reply). I also briefly discuss a valid extension to qubits given by Busch.
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- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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- It has recently been claimed by De Zela that Gleason's theorem, for probability measures on the lattice of projection operators, can be extended to qubits by adding assumptions...
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