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arXiv · 2302.09645

Transcendental properties of entropy-constrained sets: Part II

Vjosa Blakaj·Chokri Manai
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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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Vjosa Blakaj, Chokri Manai. 2023-02-19. Transcendental properties of entropy-constrained sets: Part II. https://doi.org/10.1063/5.0182728

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