Related papers: Quaternionic representation and design of depolari…
This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex…
Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's…
We study matrix forms of quaternionic versions of the Fourier Transform and Convolution operations. Quaternions offer a powerful representation unit, however they are related to difficulties in their use that stem foremost from…
The scattering of a Dirac particle has been studied for a quaternionic potential step. In the potential region an additional diffusion solution is obtained. The quaternionic solution which generalizes the complex one presents an…
We present an optical filter that transmits photon pairs only if they share the same horizontal or vertical polarization, without decreasing the quantum coherence between these two possibilities. Various applications for entanglement…
Controlling the depolarization of light is a long-standing open problem. In recent years, many demonstrations have used the polarization of single photons to encode quantum information. The depolarization of these photons is equivalent to…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
We study abelian varieties $A$ with multiplication by a totally indefinite quaternion algebra over a totally real number field and give a criterion for the existence of principal polarizations on them in pure arithmetic terms. Moreover, we…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
We attempt to get a polynomial solution to the inverse problem, that is, to determine the form of the mechanical Hamiltonian when given the energy spectrum and transition dipole moment matrix. Our approach is to determine the potential in…
Polaritons in semiconductor microcavities are hybrid quasiparticles consisting of a superposition of photons and excitons. Due to the photon component, polaritons are characterized by a quantum coherence length in the several micron range.…
This is an addition to a series of papers [FL1, FL2, FL3, FL4], where we develop quaternionic analysis from the point of view of representation theory of the conformal Lie group and its Lie algebra. In this paper we develop split…
We present a method to characterize the polarization state of a light field in the continuous-variable regime. Instead of using the abstract formalism of SU(2) quasidistributions, we model polarization in the classical spirit by superposing…
Due to the non-commutative nature of quaternions we introduce the concept of left and right action for quaternionic numbers. This gives the opportunity to manipulate appropriately the $H$-field. The standard problems arising in the…
Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial…
The ability to filter quantum states is a key capability in quantum information science and technology, in which one-qubit filters, or polarizers, have found wide application. Filtering on the basis of entanglement requires extension to…
Quaternions are an important tool to describe the orientation of a molecule. This paper considers the use of quaternions in matching two conformations of a molecule, in interpolating rotations, in performing statistics on orientational…
Polarization is a useful probe to investigate the geometries and dynamics of outflow in BAL QSOs. We perform a Monte-Carlo simulation to calculate the polarization produced by resonant and electron scattering in BALR. We find: 1)A rotated…
Optical polarizers are essential components for the selection and manipulation of light polarization states in optical systems. Over the past decade, the rapid advancement of photonic technologies and devices has led to the development of a…
We show how to prepare four-photon polarization entangled states based on some Einstein-Podolsky-Rosen (EPR) entanglers. An EPR entangler consists of two single photons, linear optics elements, quantum non-demolition measurement using a…