Related papers: General approach to SU(n) quasi-distribution funct…

The time operator canonically conjugated to the Hamiltonian of $N$ interacting particles on the line is constructed using SU(1,1) as a dynamical symmetry. This hidden conformal symmetry enables us to make a group theoretic analysis of the…

We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…

We propose a practical recipe to compute the ${s}$-parametrized maps for systems with $SU(1,1)$ symmetry using a connection between the ${Q}$ and ${P} $ symbols through the action of an operator invariant under the group. The particular…

Geometric Phase in Quantum Mechanics is generally formulated entirely in terms of geometric structure of the Complex Hilbert Space. We will exploit this fact in case of mixed states for three level open systems undergoing depolarization…

In analogy to the classical isomorphism between $\mathcal{L}(\mathcal{S}(\mathbb{R}^{n}) ,\mathcal{S}^{\prime}(\mathbb{R}^{m}) ) $ and $\mathcal{S}^{\prime}(\mathbb{R}^{n+m}) $, we show that a large class of moderate linear mappings acting…

Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…

Usually models for quantum computations deal with unitary gates on pure states. In this paper we generalize the usual model. We consider a model of quantum computations in which the state is an operator of density matrix and the gates are…

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.

We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…

We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…

The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…

In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional operator $\mathbf{P}$ consisting of finitely or countably many distributional operators $P_n$, which are…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

Focusing particularly on one-qubit and two-qubit systems, I explain how the quantum state of a system of n qubits can be expressed as a real function--a generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase space is…

The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…

We discuss when an operator, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. To the contrary to…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…

We consider the construction of the basic bundle gerbe on SU(n) introduced by Meinrenken and show that it extends to a range of groups with unitary actions on a Hilbert space including U(n), diagonal tori and the Banach Lie group of unitary…

In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…