2010/04/30 by Christoph Spengler, Marcus Huber, Beatrix C. Hiesmayr +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Dimension (graph theory) #Linear subspace #Matrix (chemical analysis) #Measure (data warehouse) #Orthonormal basis #Parameterized complexity #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Rank (graph theory) #Unitary matrix #Unitary state #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8113/43/38/385306
published as J. Phys. A: Math. Theor. 43, 385306 (2010) · 13 pages, 1 figure
arxiv created 2010/07/14 · openalex publication_date 2010/08/17 · arxiv updated 2010/08/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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).