Ranks and eigenvalues of states with prescribed reduced states

Chi-Kwong Li, Yiu-Tung Poon, Xuefeng Wang

For a quantum state represented as an $n\times n$ density matrix $\sigma \in M_n$, let $\mathcal{S}(\sigma )$ be the compact convex set of quantum states $\rho =({\rho }_{ij})\in M_{m\cdot n}$ with the f…