= Entanglement monotone
{title2=$\sum_r p_r E(\rho_r)\leq E(\rho)$}
An entanglement monotone quantifies <entanglement> without increasing on average under <local operations and classical communication>. The average is over recorded <quantum measurement> outcomes: individual successful branches can have more entanglement, provided their probabilities compensate for that increase. This distinction makes an entanglement monotone useful for bounding probabilistic state conversion. A pure-state entanglement monotone need only satisfy this inequality on pure input states and pure conditional branches, with local measurement outcomes refined to individual <Kraus operators>.
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