Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 323 / 1 / b / i / 2 / Solution

The Bell state $|{\Phi }^{+}⟩=(|00⟩+|11⟩)/\sqrt{2}$ has two nonzero Schmidt coefficients. Since the density operator is pure, every ensemble decomposition uses vectors in the same one-dimensional support, and hence