Entanglement of truncated quantum states

We investigate the impact of Hilbert-space truncation upon the entanglement of an initially maximally entangled $m\times m$ bipartite quantum state, after propagation under an entanglement-preserving $n\times n$ ($n\ge m$) unitary. Truncation – physically enforced, e.g., by a detector’s finite cross section – projects the state onto an $s\times s$-dimensional subspace ($3\leq s \leq n$). 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 $s$.