Past exam of the computer science course of the University of Oxford / 2022 / Quantum information / 3 / a / Solution

The two conditions on a density matrix are positive semidefiniteness and unit trace:Here positive semidefinite includes being a Hermitian matrix, with $v^{†}\rho v\ge 0$ for every vector $v$. Equivalently, a density matrix is Hermitian with nonnegative eigenvalues summing to one.