Density matrices as polarization vectors

S Kryszewski, M Zachciał

We use polarization operators known from the quantum theory of angular momentum to expand the ( N × N )-dimensional density operators. Thereby we construct generalized Bloch vectors representing density matrices. We study their properties and derive positivity conditions for any N . We also apply the procedure to study Bloch vector space for a qubit and a qutrit.

Stanisław Kryszewski, M Zachciał

We use polarization operators known from quantum theory of angular momentum to expand the $N \times N$ dimensional density operators. Thereby, we construct generalized Bloch vectors representing density matrices. We study their properties and derive positivity conditions for any $N$. We also apply the procedure to study Bloch vector space for a qubit and a qutrit.

E. Brüning, H. Mäkelä, A. Messina +1 more

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.

B. Z. Kopeliovich