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quant-ph2026
Singularising preserving countable additivity quantum channels on quantum measurable cardinals
Sviatoslav V. Dzhenzher
We investigate the structural and dynamical properties of a class of quantum channels on von Neumann algebras induced by averaging over operator groups via the Pettis integral. Uti…
quant-ph2026
Quantum channels preserving sigma-additivity and Ulam measurable cardinals
S. V. Dzhenzher
This paper investigates the interplay between the properties of quantum states on the Hilbert space \(\ell_2(κ)\) and the set-theoretic nature of the cardinal . We focus on th…
quant-ph2026
Banach and counting measures, and dynamics of singular quantum states generated by averaging of operator random walks
E. A. Dzhenzher, S. V. Dzhenzher, V. Zh. Sakbaev
In this paper the random channels and their compositions in the space of quantum states are studied. For compositions of i.i.d. random unitary channels, the limit behaviour of prob…