Concentration of measure for entropy in the BKM ensemble

Prove that the von Neumann entropy of random density matrices sampled from the Bogoliubov–Kubo–Mori (BKM) ensemble concentrates around its average in the large-dimension limit, establishing rigorous concentration-of-measure results for S(ρ) under the BKM-induced volume measure.

Background

Using the proposed sampling algorithm, the authors numerically observe that the distribution of von Neumann entropy for BKM random states is approximately Gaussian and that its standard deviation decreases with dimension, suggesting concentration of measure.

Although similar concentration phenomena are known for Hilbert–Schmidt and Bures–Hall ensembles, a formal proof for the BKM ensemble has not been established; the authors explicitly leave this as an open conjecture.