  We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states
distillable from pure multipartite states by local operations and classical
communication (LOCC). Our proof is based on a modification of a combinatorial
argument used in the fast matrix multiplication algorithm of Coppersmith and
Winograd. Previous use of methods from algebraic complexity in quantum
information theory concerned transformations with stochastic local operations
and classical operation (SLOCC), resulting in an asymptotically vanishing
success probability. In contrast, our new protocol works with asymptotically
vanishing error.
