Related papers: Kraus operators and symmetric groups
We present a brief introduction to the theory of operator limits of random matrices to non-experts. Several open problems and conjectures are given. Connections to statistics, integrable systems, orthogonal polynomials, and more, are…
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering. In decision theory, they can model…
The universal enveloping algebra U(g) of a Lie algebra g acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or "quantum group") is a deformation of a universal…
Algebraic framework for construction of a commuting set of operators that can be interpreted as integrals of motion of the open spin chain with boundary conditions and nearest neighbour interaction is investigated.
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
The necessity and utility of considering the interaction of a quantum system with its environment when describing its time evolution have been recognized in several branches of physics and of other sciences. The Kraus' representation is a…
We introduce a classification of simple, regular, closed symmetric operators with deficiency indices (1,1) according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized…
Quantum operations are usually defined as completely positive (CP), trace preserving (TP) maps on quantum states, and can be represented by operator-sum or Kraus representations. In this paper, we calculate operator-sum representation and…
We propose a taxonomy for quantum algorithms grounded in the fundamental symmetries, both continuous and discrete, underlying quantum state spaces, oracles, and circuit dynamics. By organizing algorithms according to their symmetry groups…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
Representations of the operator system determined by the canonical generators of the free product of two cyclic groups of order $2$ and $k$, or $d$ cyclic groups of order $2$, are studied for the purpose of shedding light on the…
We will investigate the norm closure of the unitary and similarity orbits of normal operators in unital, simple, purely infinite C*-algebras. An operator theoretic proof will be given to the classification of when two normal operators are…
We review the geometrical formulation of Quantum Mechanics to identify, according to Klein's programme, the corresponding group of transformations. For closed systems, it is the unitary group. For open quantum systems, the semigroup of…
In this paper, we investigate the relation between the Deddens and spectral radius algebras of two bounded linear operators, noting a similarity between them. Additionally, we characterize the Deddens and spectral radius algebras related to…
We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads by Moerdijk and Weiss. An infinity-operad is a dendroidal set D satisfying certain lifting conditions. In this paper we give a…
We formulate a general framework for the study of operator systems arising from discrete groups. We study in detail the operator system of the free group on $n$ generators, as well as the operator systems of the free products of finitely…
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
Quantum estimation of the operators of a system is investigated by analyzing its Liouville space of operators. In this way it is possible to easily derive some general characterization for the sets of observables (i.e. the possible quorums)…