Necessity of the entropy-dependent term in the single-copy model

Determine whether the entropy-dependent term in the sample-complexity upper bound for single-copy estimation of the state frame potential is necessary.

Background

In the single-copy sample model, the paper gives a store-and-estimate algorithm whose sample complexity depends on a Rényi entropy of the ensemble-weight distribution. The paper does not establish a matching lower bound for this entropy-dependent contribution and explicitly poses its necessity as an open problem.