On the nonclassicality distance indicator of qudits

We consider the nonclassicality distance indicator of a state in finite-dimensional quantum systems which is evaluating a state nonclassicality by its remoteness from the set of "classical states". The latter are identified with those states whose Wigner function is non-negative. The corresponding Wigner function's positivity polytope in the simplex of qudit eigenvalues is introduced and the representation for the nonclassicality distance indicator as a piecewise function is derived. The results are exemplified by the qutrit case.