2 problems

Carlen–Lieb–Reuvers conjecture. The Hilbert–Schmidt norm of the $k$-particle reduced density matrix is maximised by Slater determinants, equivalently,

Let $Phi\in\mathfrak{h}\wedge\mathfrak{h}$ be normalized with canonical form … Write $\lambda_{\max}=\sup_{k}\lambda_k$. Highly correlated regime conjecture. There exists a constan…