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Comment on "Gleason-Type Theorem for Projective Measurements, Including Qubits" by F. De Zela
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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 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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Gleason's Theorem for a Qubit as Part of a Composite System
Any probability assignment to qubit measurements that is consistent with embedding the qubit in a larger composite system is given by a density matrix via the Born rule.
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