= Entanglement dilution
Entanglement dilution uses <local operations and classical communication> to prepare partially entangled states from <maximally entangled states>, such as <Bell pairs>. For many identical bipartite pure targets, the asymptotic cost in Bell pairs per target, allowing a vanishing approximation error, is their <entanglement entropy> in bits. The <quantum typical subspace> of the target's <Schmidt coefficients> has almost all its weight and dimension at most $2^{m(S+\delta)}$. A maximally entangled state of this dimension can be converted to the normalized truncated target by <Nielsen's pure-state conversion theorem>. The resulting state approaches the full target as the retained weight tends to one. <Average monotonicity of pure-state entanglement entropy> and entropy continuity give the converse lower bound. This is the reverse asymptotic task to <entanglement concentration>.
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