Hi guys,
I'm currently carrying out an undergraduate project studying the Renyi-2 entropy of superpositions of Haar-random, Clifford and Gaussian states. Specifically, I'm plotting the mean entropy of the equal weight superposition for a randomly generated set of states from each family seperately, and comparing that to the mean Renyi-2 of the individual states. For Cliffords, I'm finding that the superposition Renyi-2 entropy approaches and then decreases well below the Haar-random single-state entropy, but I feel like that can't make any sense, because I thought superpositions of Cliffords would begin to act more uniformly random like Haar-random states, and converge to the Haar single-state entropy. My supervisor agrees with me on this as well. However, I've checked over all my code several times, and I can't see any errors in it.
I've attached two rough plots (apologies for the quality of the second in particular, it's a rough version, but the figures should be implemented correctly). Any help would be greatly appreciated, as I've been dealing with this issue for nearly two weeks now, and I'm running out of ideas as to what I could be doing wrong.