3 citations · 5 across the 14 of their papers we have counts for
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Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps
Sviatoslav V. Dzhenzher
The classical Kolmogorov--Arnold representation theorem states that any continuous multivariate function can be exactly decomposed into a finite composition of univariate continuou…
Algebraic Kolmogorov--Arnold representation theorem for quantum measurement
Sviatoslav V. Dzhenzher
We establish an operational framework connecting the classical Kolmogorov--Arnold (KA) representation theorem to quantum information theory. By introducing and proving an algebraic…
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…
Quantum channels preserving sigma-additivity on diagonal von Neumann algebras 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 the…
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…