= Nielsen's pure-state conversion theorem
{c}
{title2=$|\psi\rangle\xrightarrow{\mathrm{LOCC}}|\phi\rangle\iff\lambda(\psi)\prec\lambda(\phi)$}
An exact deterministic <LOCC> conversion of a bipartite pure state to another is possible exactly when the input vector of squared <Schmidt coefficients> is majorized by the output vector. Sort the two probability vectors decreasingly and pad with zeros to a common length before applying <majorization>. A maximally entangled state may therefore be converted to a product state, while the reverse conversion is forbidden. The criterion does not assert conversion by postselection or with a catalyst.
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