A general method for implementing multipartite unitary operations that are close to the identity using a small amount of entanglement and classical communication is presented. For cases where methods were previously known, our approach requires less entanglement. In addition, it is shown that, via compression, the average communication required from all parties except one may be reduced to the same as the entanglement. This improves upon previous methods which required a large amount of communication that did not scale down with the strength of the interaction.
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