On Families of Wigner Functions for N-Level Quantum Systems

A method for constructing all admissible unitary non-equivalent Wigner quasiprobability distributions providing the Stratonovic-h-Weyl correspondence an arbitrary N-level quantum system is proposed. The based on reformulation of Stratonovich–Weyl in form algebraic “master equations” spectrum kernel. later implements a map between operators Hilbert space and functions phase identified by complex flag manifold. non-uniqueness solutions to master equations leads diversity among distributions. It shown that possible kernels N=(2j+1)-level system, one can always identify representative realizes so-called SU(2)-symmetric spin-j symbol correspondence. exemplified considering single qubit qutrit.