01508nas a2200145 4500008004100000245005300041210005300094260001500147520109300162100001801255700001801273700002001291700001401311856003701325 2012 eng d00aMinimum Entangling Power is Close to Its Maximum0 aMinimum Entangling Power is Close to Its Maximum c2012/10/043 a 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.
1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David, W1 aZeng, Bei uhttp://arxiv.org/abs/1210.1296v1