Kenfack – Życzkowski indicator of nonclassicality for two non-equivalent representations of Wigner function of qutrit

Following Kenfack and Życzkowski, we consider the indicator of nonclassicality of quantum states for N−level systems defined via the integral of the absolute value of the Wigner function. For these systems, remaining in the framework of Stratonovich-Weyl correspondence, one can construct a whole family of representations of the Wigner functions defined over the continuous phase-space and characterized by a set of (N−2) moduli parameters. It is shown that the nonclassicality indicator, being invariant under the SU(N) transformations of states, turns to be sensitive to the representation of the Wigner function. We analyse this representation dependence computing the Kenfack-Życzkowski indicators for pure and mixed states of a 3-level system using a generic and two degenerate Stratonovich-Weyl kernels respectively. Our calculations reveal three classes of states: the “absolutely classical/quantum” states, which have zero and non-vanishing indicator for all values of the moduli parameters correspondingly, and the “relatively quantum-classical” states whose classicality/quantumness is susceptible to a representation of the Wigner function. Herewith, all pure states of qutrit belong to the “absolutely quantum” states. © 2021 Elsevier B.V.