9 papers
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 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…
The Strong Law of Large Numbers for random semigroups with unbounded generators on uniformly smooth Banach spaces
S. V. Dzhenzher, V. Zh. Sakbaev
We consider random linear unbounded operators on a Banach space . For example, such random operators may be random quantum channels. The Law of Large Numbers is known…
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…
Limit theorems for the evolution of quantum pure states
S. V. Dzhenzher, V. Zh. Sakbaev
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
The Strong Law of Large Numbers for random semigroups on uniformly smooth Banach spaces
S. V. Dzhenzher, V. Zh. Sakbaev
We consider random linear continuous operators on a Banach space . For example, such random operators may be random quant…