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arXiv · 0806.1174

Bloch vectors for qudits

Reinhold A. Bertlmann·Philipp Krammer
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Abstract

We present three different matrix bases that can be used to decompose density matrices of $d$--dimensional quantum systems, so-called qudits: the \emph{generalized Gell-Mann matrix basis}, the \emph{polarization operator basis}, and the \emph{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 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.

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Reinhold A. Bertlmann, Philipp Krammer. 2008-06-06. Bloch vectors for qudits. https://doi.org/10.1088/1751-8113/41/23/235303

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