相关论文: On the completeness of a system of coherent states
The von Neumann type subsystems of $q$-deformed coherent states are considered. The completeness of such subsystems is proved.
Standart Coherent State Systems have an analysis based on lattices (von Neumann's lattices) in terms of wich they are classified, looking at the size of the minimun cell, by: complete, overcomplete and not complete. In this work we analize…
Condition for distinguishability of countably infinite number of pure states by a single measurement is given. Distinguishability is to be understood as possibility of an unambiguous measurement. For finite number of states, it is known…
In the paper our aim was to study the properties of a new version of coherent states whose argument is a linear combination of two special singular square 2 x 2 matrix, having a single nonzero element, equal to 1, and two labeling complex…
Let $G$ be a nilpotent Lie group and let $\pi$ be a coherent state representation of $G$. The interplay between the cyclicity of the restriction $\pi|_{\Gamma}$ to a lattice $\Gamma \leq G$ and the completeness of subsystems of coherent…
We investigate the completeness of Gabor systems with respect to several classes of window functions on rational lattices. Our main results show that the time-frequency shifts of every finite linear combination of Hermite functions with…
Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…
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…
The affine coherent states quantization is a promising integral quantization of Hamiltonian systems when the phase space includes at least one conjugate pair of variables which takes values from a half-plane. Such a situation is common for…
Recently, based on a supersymmetric approach, new classes of conditionally exactly solvable problems have been found, which exhibit a symmetry structure characterized by non-linear algebras. In this paper the associated ``non-linear''…
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…
We define coherent states carrying SU(N) charges by exploiting generalized Schwinger boson representation of SU(N) Lie algebra. These coherent states are defined on $2 (2^{N - 1} - 1)$ complex planes. They satisfy continuity property and…
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the…
In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], of an electron moving in a plane in uniform external magnetic and electric fields which possesses both discrete and…
A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in…
We examine the circuit complexity of coherent states in a free scalar field theory, applying Nielsen's geometric approach as in [1]. The complexity of the coherent states have the same UV divergences as the vacuum state complexity and so we…
We construct a family of coherent states transforms attached to generalized Bargmann spaces [C.R. Acad.Sci.Paris, t.325,1997] in the complex plane. This constitutes another way of obtaining the kernel of an isometric operator linking the…
The canonical coherent states are expressed as infinite series in powers of a complex number $z$ in their infinite series version. In this article we present classes of coherent states by replacing this complex number $z$ by other choices,…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
We construct a class of coherent spin-network states that capture proprieties of curved space-times of the Friedmann-Lama\^itre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular…