Matrix-element distributions as a signature of entanglement generation

We explore connections between an operator’s matrix-element distribution and its entanglement generation. Operators with matrix-element distributions similar to those of random matrices generate states of high multipartite entanglement. This occurs even when other statistical properties of the operators do not coincide with random matrices. Similarly, operators with some statistical properties of random matrices may not exhibit random matrix element distributions and will not produce states with high levels of multipartite entanglement. Finally, we show that operators with similar matrix-element distributions generate similar amounts of entanglement.