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I've been looking into the structure of the Bloch sphere for qudits, and I am wondering if there is a transformation matrix (or rotation matrix) formula corresponding to high-dimensional quantum states like qutrits.

I prefer to write the density matrix on the basis of Weyl's operators, and I found that the corresponding 8-dimensional transformation matrix referring to Wely's operators is in a manner close to the qubit case. However, it is much more complicated to find a parametric transformation matrix to include all or most unitary operations in state space. Is there a possible solution to this question?

glS
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Waing
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  • unitary operators act like special orthogonal matrices on the generalised $n$-dimensional Bloch representation, see eg https://quantumcomputing.stackexchange.com/a/23366/55. Are you asking how to parametrise unitary matrices in general, or how to parametrise orthogonal ones? – glS Jul 06 '22 at 12:52
  • Thank you for your reply. I'm trying to parametrise the 8*8 special orthogonal matrices which correpond to all unitary operations on qutrits. – Waing Jul 06 '22 at 14:02

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