Entropy versus isotropy

Determine whether the isotropy floor remains at least as large as the amortized stabilizer Rényi entropy lower bound for every number of qubits.

Background

The isotropy floor and the amortized stabilizer Rényi entropy provide distinct efficiently or inefficiently computable lower bounds on T-count. The isotropy floor is larger on all tested pure-cubic gates through six qubits and on the named families examined in the paper.

Asymptotic upper bounds on the two quantities leave open the possibility that the entropy bound eventually exceeds the isotropy floor. Computational hill-climbing has not found such an example.