An algorithm for minimum Tsallis entropy coupling

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.