Related papers: The Complete Positivity of Classical Polarization …
A parametrization of 3x3 unitary matrices is presented. This mathematical approach is inspired on polarization algebra and is formulated through the identification of a set of three orthonormal three-dimensional Jones vectors representing…
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting an expansive list of examples from the…
General properties of the differential cross section and of the polarization observables are derived for the $e^++e^-\to N+\bar N$ reaction, in presence of two--photon exchange. Polarization effects are investigated for longitudinally…
A direct calculation of the elements of the photon polarization vector for arbitrary momentum in the helicity basis shows that it is not a vector but a complex bivector. The bivector real and imaginary parts can be directly equated with…
The recent PVLAS experiment observed the rotation of polarization and the ellipticity when a linearly polarized laser beam passes through a transverse magnetic field. The phenomenon cannot be explained in the conventional QED. We attempt to…
We propose a definition of purity for positive linear maps between Euclidean Jordan Algebras (EJA) that generalizes the notion of purity for quantum systems. We show that this definition of purity is closed under composition and taking…
Polarization state of biphoton light generated via collinear frequency-degenerate spontaneous parametric down-conversion is considered. A biphoton is described by a three-component polarization vector, its arbitrary transformations relating…
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…
Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…
A general theory of optical forces on moving bodies is here developed in terms of generalized/4x4 transfer and scattering matrices. Results are presented for a planar dielectric multilayer of arbitrary refractive index placed in an…
When a photon with well-defined polarization and momentum passes through a focusing device, these properties are no longer well defined. Their loss is captured by describing polarization by a 3x3 effective density matrix. Here we show that…
Birefringent crystals are extensively used to manipulate polarized light. The generalized transfer matrix developed allows efficient calculation of the full polarization state of light transmitted through and reflected by a stack of…
Modern digital crosscorrelators permit the simultaneous measurement of all four Stokes parameters. However, the results must be calibrated to correct for the polarization transfer function of the receiving system. The transfer function for…
We construct a large class of quantum "d x d" states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic…
Up till now, the Jones vector is, strictly speaking, only a notion about the state of polarization of plane electromagnetic waves though it is generally applied to paraxial fields approximately. Here we generalize it to non-paraxial fields.…
In this paper, some tensor commutation matrices are expressed in termes of the generalized Pauli matrices by tensor products of the Pauli matrices.
This tutorial provides an overview of the local description of polarization for nonparaxial light, for which all Cartesian components of the electric field are significant. The polarization of light at each point is characterized by a $3$…
Given linear spaces $E$ and $F$ over the real numbers or a field of characteristic zero, a simple argument is given to represent a symmetric multilinear map $u(x_1, x_2, \ldots, x_n)$ from $E^n$ to $F$ in terms of its restriction to the…
We present a complete polarization characterization of any quantum state of two orthogonal polarization modes, and give a systematic measurement procedure to collect the necessary data. Full characterization requires measurements of the…
Using the Jones matrix formalism, crystal optical properties of inhomogeneous material consisting of a pile of weakly birefringent plates are analysed in relation to the cell model adopted in polarization tomography of 3D dielectric tensor…