Related papers: Transcendental properties of entropy-constrained sets: Part II

Transcendental properties of entropy-constrained sets: Part II

URL: http://arxiv.org/abs/2302.09645v2
Date: Thu, 14 Sep 2023 14:41:08 GMT
Title: Transcendental properties of entropy-constrained sets: Part II
Authors: Vjosa Blakaj and Chokri Manai
Abstract summary: We study the properties of the level sets of relative entropy, mutual information, and R'enyi entropies. Our results rule out (semi)algebraic single-shot characterizations of these entropy measures with bounded ancilla for both the classical and quantum cases.
Score: 0.0
License: http://creativecommons.org/licenses/by-nc-sa/4.0/
Abstract: In this work, we address the question of the impossibility of certain single-letter formulas by exploiting the semi-algebraic nature of various entropy-constrained sets. The focus lies on studying the properties of the level sets of relative entropy, mutual information, and R\'{e}nyi entropies. We analyze the transcendental structure of the set of states in which one of the aforementioned entropy quantities is fixed. Our results rule out (semi)algebraic single-shot characterizations of these entropy measures with bounded ancilla for both the classical and quantum cases.

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