Tight entropy bound based on p-quasinorms

TL;DR

This paper establishes tight bounds for Shannon and von Neumann entropy using p-norms, providing new methods for entropy estimation, finiteness criteria, and bounds on entropy differences, supported by numerical tests.

Contribution

It introduces a family of tight entropy bounds based on p-norms, offering improved estimates and criteria for entropy analysis.

Findings

Derived tight upper and lower entropy bounds using p-norms

Provided criteria for entropy finiteness based on p-norms

Numerical tests demonstrate the efficiency of the proposed bounds

Abstract

In the present paper we prove a family of tight upper and lower bounds for the Shannon entropy and von Neumann entropy based on the p-norms. This allows us to have an entropy estimate, a criterion for the finiteness of it and a bound on the difference of entropy, additionally, we did some numerical tests that show the efficiency of our approximations.