Wigner quasi-probability distribution for symmetric multi-quDit systems and their generalized heat kernel

• URL: http://arxiv.org/abs/2507.14866v1
• Date: Sun, 20 Jul 2025 08:26:28 GMT
• Title: Wigner quasi-probability distribution for symmetric multi-quDit systems and their generalized heat kernel
• Authors: Manuel Calixto, Julio Guerrero,
• Abstract summary: We analyze the phase-space structure of Schr"odinger $U(D)$-spin cat states.<n>We compute the generalized heat kernel relating two quasi-probability distributions $mathcalF(s)_rho$ and $mathcalF(s')_rho$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: For a symmetric $N$-quDit system described by a density matrix $\rho$, we construct a one-parameter $s$ family $\mathcal{F}^{(s)}_\rho$ of quasi-probability distributions through generalized Fano multipole operators and Stratonovich-Weyl kernels. The corresponding phase space is the complex projective ${C}P^{D-1}=U(D)/U(D-1)\times U(1)$, 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 Schr\"odinger $U(D)$-spin cat (parity adapted coherent) states and we provide plots of the corresponding Wigner $\mathcal{F}^{(0)}_\rho$ 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 $\mathcal{F}^{(s)}_\rho$ and $\mathcal{F}^{(s')}_\rho$, 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 $N\to\infty$, 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.

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