Pauli algebraic forms of normal and nonnormal operators

Abstract

A unified treatment of the Pauli algebraic forms of the linear operators defined on a unitary linear space of two dimensions over the field of complex numbers C 1 is given. The Pauli expansions of the normal and nonnormal operators, unitary and Hermitian operators, orthogonal projectors, and symmetries are deduced in this frame. A geometrical interpretation of these Pauli algebraical results is given. With each operator, one can associate a generally complex vector, its Pauli axis. This is a natural generalization of the well-known Poincaré axis of some normal operators. A geometric criterion of distinction between the normal and nonnormal operators by means of this vector is established. The results are exemplified by the Pauli representations of the normal and nonnormal operators corresponding to some widespread composite polarization devices.

Mueller Matrix Polarizing Power

“…Diattenuators constitute a subclass of nondepolarizing systems characterized by the fact that they produce differential intensity attenuation on their two polarization eigenstates. Diattenuators whose Mueller matrix is symmetric are called normal [53][54][55][56] or homogeneous [1].…”

Universal Synthesizer of Mueller Matrices Based on the Symmetry Properties of the Enpolarizing Ellipsoid

“…Pure Mueller matrices always satisfy D = P [32]. When m R = I 3 , then M J is usually denoted as M D and corresponds to a normal diattenuator [33,34] (or homogeneous diattenuator [35]), while D = 0 (i.e., zero diattenuation-polarizance and m = m R ) is characteristic of retarders, which are denoted as M R [30].…”

Degree of polarization as a measurable quantity for a quantum optical field containing variously polarized photons

“…It can be understood as an operator describing a linear polarizer [15]. The contrast of intensity takes the form:…”

“…Consider, for example, a beam containing only linearly polarized photons -according to (15) We can also present a formal analogy between classical and quantum theory by considering a quantum correlation function, defined by Glauber [11] as coincidence between photon detection at two points in space for two moments in time:…”