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We consider two capacity quantities associated with bipartite unitary gates:the entangling and the disentangling power. For two-qubit unitaries these twocapacities are always the same. Here we prove that these capacities aredifferent in general. We do so by constructing an explicit example of aqubit-qutrit unitary whose entangling power is maximal (2 ebits), but whosedisentangling power is strictly less. A corollary is that there can be nounique ordering for unitary gates in terms of their ability to performnon-local tasks. Finally we show that in large dimensions, almost all bipartiteunitaries have entangling and disentangling capacities close to the maximalpossible (and thus in high dimensions the difference in these capacities issmall for almost all unitaries).Comment: 6 pages, 1 airfoi

Entangling and Disentangling Power of Unitary Transformations Are Not Equal