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