2025/07/20 by Calixto, Manuel, Guerrero, Julio
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2507.14866
For a symmetric N-quDit system described by a density matrix ρ, we construct a one-parameter s family F(s)ρ of quasi-probability distributions through generalized Fano multipole operators and Stratonovich-Weyl kernels. The corresponding phase space is the complex projective CPD-1=U(D)/U(D-1)× U(1), related to fully symmetric irreducible representations of the unitary group U(D). For the particular cases D=2 (qubits) and D=3 (qutrits), we analyze the phase-space structure of Schrödinger U(D)-spin cat (parity adapted coherent) states and we provide plots of the corresponding Wigner F(0)ρ function. We examine the connection between non-classical behavior and the negativity of the Wigner function. We also compute the generalized heat kernel relating two quasi-probability distributions F(s)ρ and F(s')ρ, with t=(s'-s)/2 playing the role of ``time'', together with their twisted Moyal product in terms of a trikernel. In the thermodynamic limit N→∞, we recover the usual Gaussian smoothing for s'>s. A diagramatic interpretation of the phase-space construction in terms of Young tableaux is also provided.