A composite parameterization of unitary groups, density matrices and subspaces

Autor(en)

Christoph Spengler, Marcus Huber, Beatrix Hiesmayr

Abstrakt

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(en)

Teilchenphysik

Journal

Journal of Physics A: Mathematical and Theoretical

Band

43

Anzahl der Seiten

11

ISSN

1751-8113

DOI

https://doi.org/10.1088/1751-8113/43/38/385306

Publikationsdatum

2010

Peer-reviewed

Ja

ÖFOS 2012

103034 Teilchenphysik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/a-composite-parameterization-of-unitary-groups-density-matrices-and-subspaces(ad8410da-cba3-4e3f-a20a-cfa7a063bbc0).html