摘要
在信息论领域,求解2个随机变量的最小联合信息熵是一个重要的开放问题。本文首次探讨了最小联合Tsallis信息熵问题及其理论性质,给出反例证明了无法将针对香农熵的近似算法推广到量子纠缠系统的Tsallis熵。针对此问题,创新地提出了一种基于供求匹配的贪心算法,并利用受控理论证明了所提出的新算法可以控制在所有系统中求解最小联合Tsallis熵问题的近似误差。
In the field of information theory,seeking the minimum entropy coupling of two random variables is an important open problem.This paper explores the minimum Tsallis entropy coupling problem and its theoretical properties for the first time.It provides counterexamples to demonstrate that the approximate algorithms for Shannon entropy cannot be extended to Tsallis entropy in quantum entangled systems.To tackle this problem,an innovative greedy algorithm based on supply-demand matching is proposed.Majorization theory is leveraged to prove that the proposed algorithm can control the approximation error in solving the minimum Tsallis entropy coupling problem across all systems.
作者
孙清扬
胡海洋
兰宗谕
王颖喆
SUN Qingyang;HU Haiyang;LAN Zongyu;WANG Yingzhe(School of Mathematical Sciences,Key Laboratory of Mathematics and Complex Systems of Ministry of Education,Beijing Normal University,Beijing 100875)
出处
《首都师范大学学报(自然科学版)》
2025年第6期26-33,共8页
Journal of Capital Normal University:Natural Science Edition
基金
国家重点研发计划项目(2020YFA0712900)
国家自然科学基金项目(11871103)
国家级大学生创新创业项目(202210027020)。
