Parametrizations of density matrices

TL;DR

This paper reviews recent methods for parametrizing finite-dimensional density matrices, focusing on Bloch-vector and Jarlskog parametrizations, and discusses their applications in quantum system dynamics and composite systems.

Contribution

It provides a comparative overview of parametrization techniques and explores their applications in quantum dynamics and composite system state construction.

Findings

Detailed discussion of Bloch-vector parametrization for time-dependent Hamiltonians

Analysis of the Bloch vector in two-qubit systems

Application of Jarlskog parametrization to construct density matrices for composite systems

Abstract

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.