2007/06/12 by Reinhold A. Bertlmann, Bertlmann, Reinhold A., Philipp Krammer +1 · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Basis (linear algebra) #Bloch sphere #Computer science #Density matrix #FOS: Physical sciences #Geometry #Hilbert space #Mathematics #Matrix (chemical analysis) #Measure (data warehouse) #Operator (biology) #Orthogonal basis #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum entanglement #Quantum mechanics #Qubit #Qutrit #Spectroscopy and Quantum Chemical Studies #quant-ph
paper · pdf · doi:10.48550/arxiv.0706.1743
published in arXiv (Cornell University) (Cornell University) · 30 pages, 4 figures
arxiv created 2007/06/12 · openalex publication_date 2007/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present three different matrix bases that can be used to decompose density matrices of d--dimensional quantum systems, so-called qudits: the generalized Gell-Mann matrix basis, the polarization operator basis, and the Weyl operator basis. Such a decomposition can be identified with a vector --the Bloch vector, i.e. a generalization of the well known qubit case-- and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We consider the important case of an isotropic two--qudit state and decompose it according to each basis. Investigating the geometry of entanglement of special parameterized two--qubit and two--qutrit states, in particular we calculate the Hilbert--Schmidt measure of entanglement, we find that the Weyl operator basis is the optimal choice since it is closely connected to the entanglement of the considered states.