2008/05/15 by Reinhold A. Bertlmann, Reinhold A Bertlmann, Philipp Krammer · 12 citations
Computer Science · Physics and Astronomy · #Bloch sphere #Density matrix #Generalization #Matrix (chemical analysis) #Operator (biology) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum entanglement #Quantum many-body systems #Qubit #Representation (politics) #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/23/235303
published as J. Phys. A: Math.Theor. 41 (2008) 235303 · 22 pages, 1 figure, new version of paper arXiv:0706.1743 [quant-ph] containing just the Bloch vector part but enlarged with an additional section on experimental application of entanglement witnesses in 3x3 dimensions
openalex publication_date 2008/05/15 · arxiv created 2008/06/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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 present a new method to decompose density matrices via so-called standard matrices, consider the important case of an isotropic two-qudit state and decompose it according to each basis. In the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin-1 measurements, which is appropriate for an experimental realization.