Multipartite Correlated Majorization Criteria for Finite Discrete Probability

TL;DR

This paper develops a generalized majorization framework for finite discrete probability distributions in quantum information, revealing that Rényi and Burg entropies can characterize correlations and uncorrelated cases.

Contribution

It introduces a unified majorization criteria based on Rényi and Burg entropies applicable to both correlated and uncorrelated distributions.

Findings

Proves subadditivity of Rényi and Burg entropies.

Shows criteria depend solely on these entropies.

Provides characterization of entropies via continuity, symmetry, and subadditivity.

Abstract

In this paper we study multipartite and correlated majorization of the finite discrete probability distributions emerging in quantum information theory. We start proving the subadditivity of the R\'{e}nyi and Burg entropies, and we show that the criteria for such a generalized majorization scheme can be provided solely in terms of the R\'{e}nyi and Burg entropies. Surprisingly, the same set of criteria applies both to the correlated and uncorrelated cases. Finally, based on our findings in majorization, we give a proof of the characterization of the R\'{e}nyi and Burg entropies in terms of continuity, symmetry and (sub)additivity.