  We demonstrate the connection between an operator's matrix element
distribution and entangling power via numerical simulations of random,
pseudo-random, and quantum chaotic operators. Creating operators with a random
distribution of matrix elements is more difficult than creating operators that
reproduce other statistical properties of random matrices. Thus, operators that
fulfill many random matrix statistical properties may not generate states of
high multi-partite entanglement. To quantify the randomness of various
statistical distributions and, by extension, entangling power, we use
properties of interpolating ensembles that transition between integrable and
random matrix ensembles.
