Related papers: Quantum Phase Operator and Phase States
The problem of defining a hermitian quantum phase operator is nearly as old as quantum mechanics itself. Throughout the years, a number of solutions was proposed, ranging from abstract operator formalisms to phase-space methods. In this…
We demonstrate that quantum Hamiltonian operator for a free transverse field within the framework of the second quantization reveals an alternative set of states satisfying the eigenstate functional equations. The construction is based upon…
We introduce a quantum like representation of a Spiral Phase Plate, acting on an electromagnetic field, as a two mode phase operator. The representation is based on the Newton binomial expansion and on properties of rational power of…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…
A coherent state representation of the expectation value of an arbitrary (but still polynomial) normal ordered quantum operator is discussed. This serves as a basis for developing a fast and easy-to-handle algorithm, based on series of…
We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven…
We show that the three quantum states (P$\acute{o}$lya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediates states which interpolate between the…
A mixed quantum state is represented by a Hermitian positive semi-definite operator $\rho$ with unit trace. The positivity requirement is responsible for a highly nontrivial geometry of the set of quantum states. A known way to satisfy this…
In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the…
The Wigner Phase Operator (WPO) is identified as an operator valued measure (OVM) and its eigen states are obtained. An operator satisfying the canonical commutation relation with the Wigner phase operator is also constructed and this…
We define a unitary phase operator for photons in a single momentum mode. The operator acts on a Hilbert space with basis consisting of all number states in both polarizations. The Susskind Glogower operator, ${\hat{E}} = e^{i \hat{\phi}}$,…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
We review some quantum-phase descriptions of optical fields. We focus on real fields that can be generated in practice in various nonlinear optical processes. Thus, we rather avoid discussions of phase formalisms as such and try to exploit…
We discuss the presence of a geometrical phase in the evolution of a qubit state and its gauge structure. The time evolution operator is found to be the free energy operator, rather than the Hamiltonian operator.
A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…
Quantum algorithms for estimating the eigenvalues of matrices, including the phase estimation algorithm, serve as core subroutines in a wide range of quantum algorithms, including those in quantum chemistry and quantum machine learning. The…
This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0),…
The Half-Transform Ansatz (HTA) is a proposed method to solve hyper-geometric equations in Quantum Phase Space by transforming a differential operator to an algebraic variable and including a specific exponential factor in the wave…
We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a…