Entanglement of truncated quantum states

We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled m×m bipartite quantum state, after propagation under an entanglement-preserving n × n (n ≥ m) unitary. Truncation – physically enforced, e.g., by a detector's finite cross section – projects the state onto an s × s-dimensional subspace (3 ≤ s ≤ n). For a random local unitary evolution, we obtain a simple analytical formula that expresses the truncation-induced entanglement loss as a function of n, m and s.