概率性量子资源蒸馏的误差指数

中文摘要 AI 辅助

在本手稿中，我们建立了一个统一框架，用于分析在近似资源非生成仪器下概率性资源蒸馏的条件误差指数。对于满足适当结构条件的通用量子资源理论，我们推导了条件蒸馏误差指数的一般单发界限。通过将概率性蒸馏与后选择复合量子假设检验联系起来，我们进一步获得了纠缠、相干性和魔法蒸馏在有限块长度下条件误差指数的解析刻画，并推导了它们在零速率区域的渐近表达式。对于纠缠和魔法资源理论中的几个代表性态族，这些刻画简化为显式的闭式公式。将它们与相应的确定性蒸馏指数进行比较，我们确定了后选择在条件误差的指数衰减率上带来严格改进的区域。我们的结果揭示了后选择在量子资源蒸馏中的操作优势，并确立了后选择复合假设检验作为刻画概率性资源处理任务的一般工具。

英文摘要

In this manuscript, we establish a unified framework for analyzing the conditional error exponents of probabilistic resource distillation under approximately resource-nongenerating instruments. For generic quantum resource theories satisfying suitable structural conditions, we derive general oneshot bounds on the conditional distillation error exponents. By relating probabilistic distillation to postselected composite quantum hypothesis testing, we obtain bounds of the conditional error exponents for coherence distillation under finite blocklength and asymptotic zero-rate scenarios, we furthermore obtain analytical characterizations of the conditional error exponents for entanglement and magic distillation under finite blocklength and asymptotic zero-rate scenarios. For several representative families of states in entanglement and magic resource theories, these characterizations reduce to explicit closed-form formulas. Comparing them with the corresponding deterministic distillation exponents, we identify regimes in which postselection yields a strict improvement in the exponential decay rate of the conditional error. Our results reveal an operational advantage of postselection in quantum resource distillation and establish postselected composite hypothesis testing as a general tool for characterizing probabilistic resource-processing tasks.

发表机构

• College of Information Science and Technology, Beijing University of Chemical Technology（北京化工大学信息科学与技术学院）

机构由 AI 辅助整理，请以论文原文为准。