Quantum channels built from sigma-complete ultrafilters map normal states to singular sigma-additive states on ell_2(kappa) precisely when kappa is Ulam measurable.
Banachandcountingmeasures, anddynamics of singular quantum states generated by averaging of operator random walks
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Quantum channels preserving sigma-additivity and Ulam measurable cardinals
Quantum channels built from sigma-complete ultrafilters map normal states to singular sigma-additive states on ell_2(kappa) precisely when kappa is Ulam measurable.