Related papers: Properties of a Polarization based Phase Operator
Hilbert space operators may be mapped onto a space of ordinary functions (operator symbols) equipped with an associative (but noncommutative) star-product. A unified framework for such maps is reviewed. Because of its clear probabilistic…
We introduce a one-parameter generalized oscillator algebra A(k) (that covers the case of the harmonic oscillator algebra) and discuss its finite- and infinite-dimensional representations according to the sign of the parameter k. We define…
In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a…
Phase shifters are fundamental reconfigurable components in photonic circuits. In conjunction with passive elements, they control light flow and serve as foundational building blocks for diverse applications, including communication,…
In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twisting operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values $z_L$ measure the…
From relativistic point of view it has been shown here that a polarized photon can be visualized to give an equivalent spinorial description when the two-component spinor is the eigenvector of $2\times2$ Hermitian, Polarization matrix. The…
Position deformation of a Heisenberg algebra and Hilbert space representation of both maximal length and minimal momentum uncertainties may lead to loss of Hermiticity of some operators that generate this algebra. Consequently, the…
The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the…
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 present an analytical study of the spin projection operator of the spin state and the helicity state. It is pointed out emphatically that the former is Lorentz covariant, while the latter is a nonrelativistic two-component operator. In…
We revisit the quantum oscillator model of the electromagnetic field and conclude that, while the nonlocal positive and negative frequency ladder operators generate a photon Fock basis, the Hermitian field operators obtained by second…
The vector potential operator, $\hat{\boldsymbol A}$, is transformed and rewritten in terms of cosine and sine functions in order to get a clear picture of how the photon states relate to the $\boldsymbol A$ field. The phase operator,…
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…
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…
We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the…
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
The helicity flux operator is a fascinating quantity that characterizes the angular distribution of the helicity of radiative photons or gravitons and it has many interesting physical consequences. In this paper, we construct the…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…
Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…
We introduce a class of bipartite operators acting on $\mathcal{H} \otimes \mathcal{H}$ ($\mathcal{H}$ being an $n$-dimensional Hilbert space) defined by a set of $n$ Completely Different Permutations CDP. Bipartite operators are of…