We consider two capacity quantities associated with bipartite unitary gates: the entangling and the disentangling power. Here, we prove that these capacities are different in general by constructing an explicit example of a qubit-qutrit unitary whose entangling power is maximal (2 ebits), but whose disentangling power is strictly less. A corollary is that there can be no unique ordering for unitary gates in terms of their ability to perform nonlocal tasks. Finally, we show that in large dimensions, almost all bipartite unitaries have entangling and disentangling capacities close to maximal.

• Received 14 August 2008

DOI:https://doi.org/10.1103/PhysRevLett.103.030501