Past exam of the computer science course of the University of Oxford / 2023 / Quantum information / 3 / a / Solution

A bipartite pure state is entangled exactly when it is not a product state: there are no normalized quantum states $|u{⟩}_A,|v{⟩}_B$ such thatEquivalently, its Schmidt rank exceeds one, or either reduced density matrix is a mixed state. This definition concerns quantum entanglement across the specified division into systems $A$ and $B$.