Renyi extrapolation of Shannon entropy

摘要

Relations between Shannon entropy and Renyi entropies of integer order arediscussed. For any N-point discrete probability distribution for which theRenyi entropies of order two and three are known, we provide an lower and anupper bound for the Shannon entropy. The average of both bounds provide anexplicit extrapolation for this quantity. These results imply relations betweenthe von Neumann entropy of a mixed quantum state, its linear entropy andtraces.