2021/09/13 by Jun-Kai You, You, Jun-Kai, Hao–Chung Cheng +3
Computer Science · Engineering · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Optimization and Control (math.OC) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Sparse and Compressive Sensing Techniques #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2109.06054
openalex publication_date 2021/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Quantum information quantities play a substantial role in characterizing operational quantities in various quantum information-theoretic problems. We consider numerical computation of four quantum information quantities: Petz-Augustin information, sandwiched Augustin information, conditional sandwiched Renyi entropy and sandwiched Renyi information. To compute these quantities requires minimizing some order-α quantum Renyi divergences over the set of quantum states. Whereas the optimization problems are obviously convex, they violate standard bounded gradient/Hessian conditions in literature, so existing convex optimization methods and their convergence guarantees do not directly apply. In this paper, we propose a new class of convex optimization methods called mirror descent with the Polyak step size. We prove their convergence under a weak condition, showing that they provably converge for minimizing quantum Renyi divergences. Numerical experiment results show that entropic mirror descent with the Polyak step size converges fast in minimizing quantum Renyi divergences.