Sampling Matrices from Harish-Chandra-Itzykson-Zuber Densities with Applications to Quantum Inference and Differential Privacy

Jonathan Leake, Colin S. McSwiggen, Nisheeth K. Vishnoi

Given two $n\times n$ Hermitian matrices $Y$ and $\Lambda$, the Harish-Chandra-Itzykson-Zuber (HCIZ) distribution on the unitary group $\text{U}(n)$ is $e^{\text{tr}(U\Lambda U^{\ast }Y)}d\mu (U)$, whe…