Bloch vectors for qudits

Understand

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.