A composite parameterization of unitary groups, density matrices and subspaces

Christoph Spengler, Marcus Huber, Beatrix Hiesmayr

Research output: Contribution to journalArticle (Academic Journal)peer-review

31 Citations (Scopus)


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 of arbitrary dimension d which is constructed in a composite way. We show explicitly how any element of can be composed of matrix exponential functions of generalized anti-symmetric σ-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 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).
Original languageEnglish
Pages (from-to)385306
Number of pages11
JournalJournal of Physics A: Mathematical and Theoretical
Issue number38
Publication statusPublished - 24 Sep 2010


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