A composite parameterization of unitary groups, density matrices and subspaces

Author(s)
Christoph Spengler, Marcus Huber, Beatrix Hiesmayr
Abstract

Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In this paper we present a parameterization of the unitary group U(d) of arbitrary dimension d which is constructed in a composite way. We show explicitly how any element of U(d) can be composed of matrix exponential functions of generalized anti-symmetric s-matrices and one-dimensional projectors. The specific form makes it considerably easy to identify and discard redundant parameters in several cases. In this way, redundancy-free density matrices of arbitrary rank k can be formulated. Our construction can also be used to derive an orthonormal basis of any k-dimensional subspaces of C-d with the minimal number of parameters. As an example it is shown that this feature leads to a significant reduction of parameters in the case of investigating distillability of quantum states via lower bounds of an entanglement measure (the m-concurrence).

Organisation(s)
Particle Physics
Journal
Journal of Physics A: Mathematical and Theoretical
Volume
43
No. of pages
11
ISSN
1751-8113
DOI
https://doi.org/10.1088/1751-8113/43/38/385306
Publication date
2010
Peer reviewed
Yes
Austrian Fields of Science 2012
103034 Particle physics
Portal url
https://ucrisportal.univie.ac.at/en/publications/a-composite-parameterization-of-unitary-groups-density-matrices-and-subspaces(ad8410da-cba3-4e3f-a20a-cfa7a063bbc0).html