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Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices

Department of Applied Physics, University of Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
Symmetry 2020, 12(6), 1002; https://doi.org/10.3390/sym12061002
Received: 6 May 2020 / Revised: 19 May 2020 / Accepted: 10 June 2020 / Published: 12 June 2020
(This article belongs to the Special Issue Symmetry and Asymmetry in Photonics: Theory and Emerging Practice)
The information contained in an n-dimensional (nD) density matrix ρ is parametrized and interpreted in terms of its asymmetry properties through the introduction of a family of components of purity that are invariant with respect to arbitrary rotations of the nD Cartesian reference frame and that are composed of two categories of meaningful parameters of different physical nature: the indices of population asymmetry and the intrinsic coherences. It is found that the components of purity coincide, up to respective simple coefficients, with the intrinsic Stokes parameters, which are also introduced in this work, and that determine two complementary sources of purity, namely the population asymmetry and the correlation asymmetry, whose weighted square average equals the overall degree of purity of ρ. A discriminating decomposition of ρ as a convex sum of three density matrices, viz. the pure, the fully random (maximally mixed) and the discriminating component, is introduced, which allows for the definition of the degree of nonregularity of ρ as the distance from ρ to a density matrix of a system composed of a pure component and a set of 2D, 3D,… and nD maximally mixed components. The chiral properties of a state ρ are analyzed and characterized from its intimate link to the degree of correlation asymmetry. The results presented constitute a generalization to nD systems of those established and exploited for polarization density matrices in a series of previous works. View Full-Text
Keywords: density matrices; nonregularity; indices of purity; the degree of purity; symmetry; asymmetry density matrices; nonregularity; indices of purity; the degree of purity; symmetry; asymmetry
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MDPI and ACS Style

Gil, J.J. Sources of Asymmetry and the Concept of Nonregularity of n-Dimensional Density Matrices. Symmetry 2020, 12, 1002.

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