Related papers: Quantum Phase Operator and Phase States
Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
We present a new method for constructing operators in loop quantum gravity. The construction is an application of the general idea of "coherent state quantization", which allows one to associate a unique quantum operator to every function…
A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum…
This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
Corresponding to a hypergraph $G$ with $d$ vertices, a quantum hypergraph state is defined by $|G\rangle = \frac{1}{\sqrt{2^d}}\sum_{n = 0}^{2^d - 1} (-1)^{f(n)} |n \rangle$, where $f$ is a $d$-variable Boolean function depending on the…
For certain situations we give a geometrical background for quasiclassical KP calculations based on an explicit connection to quantum mechanics and the collapse of coherent states to coadjoint orbits for classical operators.
The Ermakov Lewis quantum invariant for the time dependent harmonic oscillator is expressed in terms of number and phase operators. The identification of these variables is made in accordance with the correspondence principle and the…
Gaussian states -- or, more generally, Gaussian operators -- play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial…
W consider the problem of testing if a given matrix in the Hilbert space formulation of quantum mechanics or a function in the phase space formulation of quantum theory represent a quantum state. We propose several practical criteria to…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
The kinematic time operator can be naturally defined in relativistic and nonrelativistic quantum mechanics (QM) by treating time on an equal footing with space. The spacetime-position operator acts in the Hilbert space of functions of space…
Phase operators and phase states are introduced for irreducible representations of the Lie algebra su(3) using a polar decomposition of ladder operators. In contradistinction with su(2), it is found that the su(3) polar decomposition does…
The motivation for studying non-Hermitian systems and the role of $\mathcal{PT}$-symmetry is discussed. We investigate the use of a quantum algorithm to find the eigenvalues and eigenvectors of non-Hermitian Hamiltonians, with applications…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
In this paper we study the quantum phase properties of {\it "nonlinear coherent states"} and {\it "solvable quantum systems with discrete spectra"} using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be…