Matrix Element Randomness, Entanglement, and Quantum Chaos
  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. 
Yaakov S. Weinstein, C. Stephen Hellberg