The paper gives a sufficient condition, relying on Ulam measurable cardinals, for the existence of quantum channels that turn normal states into singular yet strictly σ-additive states via Yosida-Hewitt decomposition.
On Extreme Points of Sets in Operator Spaces and State Spaces
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Singularising preserving countable additivity quantum channels on quantum measurable cardinals
The paper gives a sufficient condition, relying on Ulam measurable cardinals, for the existence of quantum channels that turn normal states into singular yet strictly σ-additive states via Yosida-Hewitt decomposition.