Given a quantum gate $U$ acting on a bipartite quantum system, its maximum

(average, minimum) entangling power is the maximum (average, minimum)

entanglement generation with respect to certain entanglement measure when the

inputs are restricted to be product states. In this paper, we mainly focus on

the 'weakest' one, i.e., the minimum entangling power, among all these

entangling powers. We show that, by choosing von Neumann entropy of reduced

density operator or Schmidt rank as entanglement measure, even the 'weakest'

entangling power is generically very close to its maximal possible entanglement

generation. In other words, maximum, average and minimum entangling powers are

generically close. We then study minimum entangling power with respect to other

Lipschitiz-continuous entanglement measures and generalize our results to

multipartite quantum systems.

As a straightforward application, a random quantum gate will almost surely be

an intrinsically fault-tolerant entangling device that will always transform

every low-entangled state to near-maximally entangled state.