Related papers: Analytic Representation of Finite Quantum Systems
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and,…
A state of a single particle can be represented by a quantum blob in the corresponding phase space, or by a cell in its 2-D subspace. Its area is frequently stated to be no less than one half of the Plank constant, implying that such a cell…
The general transformation of the product of coherent states $\prod_{i=1}^N|\alpha_i>$ to the output state $\prod_{i=1}^M|\beta_i>$ ($N=M$ or $N\neq M$), which is realizable with linear optical circuit, is characterized with a linear map…
For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two…
A method of representing probabilistic aspects of quantum systems is introduced by means of a density function on the space of pure quantum states. In particular, a maximum entropy argument allows us to obtain a natural density function…
In this paper the generalized quantum states, i.e. positive and normalized linear functionals on $C^{*}$-algebras, are studied. Firstly, we study normal states, i.e. states which are represented by density operators, and singular states,…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
We present a possible construction of coherent states on the unit circle as configuration space. In our approach the phase space is the product Z x S^1. Because of the duality of canonical coordinates and momenta, i.e. the angular variable…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
We associate a space of (formal) representations on the space of h-formal power series with coefficients in the space of smooth functions on Rd (which we call quantizations) with an action of a group on Rd by smooth diffeomorphisms. If the…
The main goal of this paper is to demonstrate the usefulness of certain ideas from System Theory in the study of problems from complex analysis. With this paper, we also aim to encourage analysts, who might not be familiar with System…
This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The…
We prove uniform versions of two classical results in analytic number theory. The first is an asymptotic for the number of points of a complete lattice $\Lambda \subseteq \mathbb{R}^d$ inside the $d$-sphere of radius $R$. In contrast to…
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being…
In this paper, we present a formalism for representing infinite systems in quantum mechanics by employing a strategy that embraces divergences rather than avoiding them. We do this by representing physical quantities such as inner products,…
Quantum teleportation is rigorously discussed with coherent entang led states given by beam splittings. The mathematical scheme of beam splitti ng has been used to study quantum communication and quantum stochastic. We d iscuss the…