The Interplay between Error, Total Variation, Alpha-Entropy and Guessing: Fano and Pinsker Direct and Reverse Inequalities

Using majorization theory via “Robin Hood” elementary operations, optimal lower and upper bounds are derived on Rényi guessing entropies with respect to either error probability (yielding reverse-Fano Fano inequalities) or total variation distance the uniform reverse-Pinsker Pinsker inequalities). This gives a general picture of how notion randomness can be measured in many areas computer science.