Past exam of the computer science course of the University of Oxford / 2023 / Quantum information / 1 / a / ii

A basic measurement is specified by an orthonormal basis $\{|b_j⟩{\}}_{j=0}^{d-1}$. The Born rule for the density matrix $\rho$ gives the outcome probabilitiesThese probabilities are nonnegative by positive semidefiniteness and sum to one by the resolution of the identity and unit trace. In the computational basis, the answers are simply the diagonal entries ${\rho }_{jj}$.^[ref]