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The Wigner function of a finite-dimensional system can be constructed via dual pairing of a density matrix with the Stratonovich-Weyl kernel. Following Kenfack and $dot{text{Z}}$yczkowski, we consider the indicator of nonclassicality of a finite-dimensional quantum system which depends on the volume of the negative part of the Wigner function. This indicator is defined over the unitary non-equivalent classes of quantum states, i.e. represents an invariant, but since for a given quantum system there is no unique Wigner function it turns to be sensitive to the choice of representations for the Wigner function. Based on the explicit parameterization of the moduli space of the Wigner functions, we compute the corresponding Kenfack-$dot{text{Z}}$yczkowski indicators of a 3-level system for degenerate, unitary non-equivalent Stratonovich-Weyl kernels.
A measure of nonclassicality of quantum states based on the volume of the negative part of the Wigner function is proposed. We analyze this quantity for Fock states, squeezed displaced Fock states and cat-like states defined as coherent superposition of two Gaussian wave packets.
We present a new quasi-probability distribution function for ensembles of spin-half particles or qubits that has many properties in common with Wigners original function for systems of continuous variables. We show that this function provides clear a
It is commonly accepted that a deviation of the Wigner quasiprobability distribution of a quantum state from a proper statistical distribution signifies its nonclassicality. Following this ideology, we introduce the global indicator $mathcal{Q}_N$ fo
A mapping between operators on the Hilbert space of $N$-dimensional quantum system and the Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner quasiprobability distribution is constructed as a dual p
We study the Weyl-Wigner transform in the case of discrete variables defined in a Hilbert space of finite prime-number dimensionality $N$. We define a family of Weyl-Wigner transforms as function of a phase parameter. We show that it is only for a sp