发表机构
Ulm University; University of Copenhagen; Center for Integrated Quantum Science and Technology (IQST)（乌尔姆大学; 哥本哈根大学; 综合量子科学与技术中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一处理量子态、信道和超映射资源的高阶量子资源框架，引入超映射资源单调性及蒸馏稀释，并应用于动力学相干性，刻画了最大兼容超映射集合及其在信道转换中的操作差异。
AI 中文摘要
我们开发了一个用于高阶量子资源的通用框架，该框架以统一的方式处理量子态、信道和超映射（也称为过程）的资源性。通过推广态和信道资源理论中已确立的概念，我们引入并研究了超映射资源单调性以及超映射的蒸馏和稀释。作为自由超映射，我们考虑了自由网络（可通过自由信道实现的超映射）、兼容超映射（在任意组合下封闭的超映射集合）以及最大自由超信道。专门针对近似信道到信道的转换，我们证明在温和假设下，相对于金刚石距离的转换误差与最坏情况下的不保真度是一致的。然后，我们将该通用框架应用于动力学相干性的资源理论，在其中确立了最大兼容超映射集合的存在性。通过用半定约束刻画这些集合，我们证明它们严格大于相应的自由网络，但并不包含所有最大自由超信道。最后，我们研究了这些集合在单发信道蒸馏和稀释中的操作性差异，为并行设置中的两项任务以及自适应设置中的稀释提供了解决方案。
英文摘要
We develop a general framework for higher-order quantum resources that treats the resourcefulness of quantum states, channels, and supermaps (also called processes) in a unified manner. By generalizing well-established concepts from resource theories of states and channels, we introduce and study supermap resource monotones and supermap distillation and dilution. As free supermaps, we consider free networks (supermaps that can be implemented with free channels), compatible supermaps (sets of supermaps closed under arbitrary composition), and maximally free superchannels. Specializing to approximate channel-to-channel conversions, we show that under mild assumptions, the conversion error with respect to the diamond distance and the worst-case infidelity coincide. We then apply the general framework to resource theories of dynamical coherence, where we establish the existence of largest sets of compatible supermaps. By characterizing these sets with semidefinite constraints, we show that they are strictly larger than the corresponding free networks but do not contain all maximally free superchannels. We finish by investigating the operational differences of these sets in one-shot channel distillation and dilution, providing solutions for both tasks in the parallel setting and for dilution in the adaptive setting.
Comments13+48 pages, comments welcome!
