Related papers: Quantum Phase Operator and Phase States
We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…
We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive operator-valued measure corresponding to the multiple-phase estimation. In particular,…
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic…
The phase estimation algorithm is so named because it allows the estimation of the eigenvalues associated with an operator. However it has been proposed that the algorithm can also be used to generate eigenstates. Here we extend this…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
The probability distribution for finding a state of the radiation field in a particular phase is described by a multitude of theoretical formalisms; the phase-sensitivity of the Wigner quasi-probability distribution being one of them. We…
Different quantum mechanical operators can correspond to the same classical quantity. Hermitian operators differing only by operator ordering of the canonical coordinates and momenta at one moment of time are the most familiar example.…
We introduce unitary quantum phase operators for material particles. We carry out a model study on quantum phases of interacting bosons in a symmetric double-well potential in terms of unitary and commonly-used non-unitary phase operators…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis…
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…
Many eigenvalue problems arising in practice are often of the generalized form $A\x=\lambda B\x$. One particularly important case is symmetric, namely $A, B$ are Hermitian and $B$ is positive definite. The standard algorithm for solving…
The equivalence of the Rivier-Margenau-Hill and Born-Jordan-Shankara phase space formalisms to the conventional operator approach of quantum mechanics is demonstrated. It is shown that in spite of the presence of singular kernels the…
The problem of defining time (or phase) operator for three-dimensional harmonic oscillator has been analyzed. A new formula for this operator has been derived. The results have been used to demonstrate a possibility of representing…
Geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper we introduce an operational geometric phase for mixed quantum states, based on…
Quantum signal processing allows for quantum eigenvalue transformation with Hermitian matrices, in which each eigenspace component of an input vector gets transformed according to its eigenvalue. In this work, we introduce the multivariate…
In an amended version of non-Hermitian interaction picture we propose to work with the states $\psi(t)$ in a dyadic representation. The control of evolution via two conjugate Schr\"{o}diner equations then renders the usual necessity of the…
In investigations of the emergence of classicality from quantum theory, a useful step is the construction of quantum operators corresponding to the classical notion that the system resides in a region of phase space. The simplest such…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…