发表机构
ETH Zurich; IBM Quantum, IBM Research Europe – Zurich; Institute for Advanced Study in Mathematics, Harbin Institute of Technology; School of Mathematics, Harbin Institute of Technology（苏黎世联邦理工学院; IBM量子，IBM欧洲研究-苏黎世; 哈尔滨工业大学数学高等研究院; 哈尔滨工业大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对单次信息论度量中优化态复杂的问题，证明用边缘分布替代最优态效果良好，且在Petz-Rényi散度等场景下仅产生可控乘法开销，为相关度量计算提供了简化方法。
AI 中文摘要
单次信息论度量通常需要对量子态进行优化，但这些优化器的形式可能很复杂，或以非线性方式依赖于初始问题。在本文中，我们证明在许多情况下，使用边缘分布替代最优态已足够好，仅会使结果产生微小变化。我们证明，对于α∈[1/2,1)阶的Petz-Rényi散度，将B上的优化态替换为边缘分布ρ_B会产生至多1/α的乘法开销；同时，我们也针对保真度给出了类似关系，并针对夹心Rényi散度的纯态或量子-经典态情况进行了讨论。
英文摘要
One-shot information theory measures often require an optimization over states, but the form of these optimizers can be complicated or depend on the initial problem in nonlinear ways. In this note, we show that in many instances using the marginal instead of the optimal state is sufficiently good and only changes the result by a small factor. We prove that for the Petz--Rényi and sandwiched--Rényi divergences of order $α\in(0,1)$, replacing the optimizing state on $B$ by the marginal $ρ_B$ results in a multiplicative overhead of at most $1/α$.
Comments12 pages, Gui-Long Jiang and Shi-Bing Li added as authors, Theorem 3.1 now holds for $α\in(0,1)$ (instead of $[1/2,1)$), Theorem 4.1 and 4.2 show the same statement for the sandwiched Rényi divergence. This generalizes the previous result that only worked for $α=1/2$ and special classes of states
