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

The state is separable. The off-diagonal terms of the two Bell state projectors have opposite signs and cancel:This is a quantum state ensemble of two pure states that are product states, with probability $1/2$ each, establishing a separable quantum state. Its correlations are classical; an ensemble decomposition into entangled states does not itself establish quantum entanglement of the density matrix.