3 citations · 5 across the 15 of their papers we have counts for
15 papers
Kolmogorov--Arnold stability for discontinuous functions
Sviatoslav V. Dzhenzher
Here we investigate the stability of the Kolmogorov--Arnold representation theorem (KART) under adversarial reparameterisations of the hidden layer for multivariate discontinuous a…
Kolmogorov--Arnold against bounded translations
Sviatoslav V. Dzhenzher
Historically originating from Hilbert's 13th problem, the Kolmogorov-Arnold representation theorem (KART) has recently experienced a major revitalisation through its applications t…
Quantum channels on duals of von Neumann algebras in the Schrödinger picture
Sviatoslav V. Dzhenzher
The theory of quantum channels is traditionally studied either on finite-dimensional state spaces or within the Heisenberg picture as completely positive maps on C^*-algebras. In t…
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…
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 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…
The Central Limit Theorem for random exponents on a Hilbert space in the Weak Operator Topology
S. V. Dzhenzher
We consider random linear continuous operators on a Hilbert space . For example, such random operators may be random quant…
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 quantu…
The law of large numbers for discrete generalized quantum channels
S. V. Dzhenzher, V. Zh. Sakbaev
We consider random linear operators acting in a -th Schatten class in a separable Hilbert space fo…
Quantum law of large numbers for Banach spaces
S. Dzhenzher, V. Sakbaev
We consider random operators for some . The law of large numbers is known in the case in the form of usual law of l…
A simpler proof of Sternfeld's Theorem
Sviatoslav Dzhenzher
In Sternfeld's work on Kolmogorov's Superposition Theorem appeared the combinatorial-geometric notion of a basic set and a certain kind of arrays. A subset …