发表机构
National Taiwan Normal University; RIKEN; The University of Michigan（台湾师范大学; 理化学研究所; 密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在测量不相容性可保持性的资源理论中，引入基于鲁棒性的度量，证明预过滤无法从不兼容湮灭信道激活可保持性（不可行定理），但后过滤可随机激活，为量子信息处理提供实用框架。
AI 中文摘要
测量不相容性是一种基本的量子资源，能够在许多量子信息任务（包括密码学和通信）中带来优势。然而，系统与环境之间不可避免的相互作用会降低甚至完全破坏测量不相容性；这样的过程被称为测量不相容性湮灭信道。最近，噪声量子动力学保持测量不相容性的能力已在测量不相容性可保持性的资源理论中被刻画。这激励了研究如何纯化测量不相容性的保持，以及如何从测量不相容性湮灭信道中激活它。为此，我们首先引入我们的度量标准，作为该资源理论中基于鲁棒性的资源单调量。我们证明，虽然预过滤操作可以增强测量不相容性可保持性，但它们不能从不相容性湮灭信道中激活它，从而确立了一个不可行定理。此外，我们明确证明，不相容性湮灭信道可以通过后过滤操作被随机激活。我们的结果为在量子信息处理中利用测量不相容性提供了一个实用框架。
英文摘要
Measurement incompatibility is a fundamental quantum resource that enables advantages in many quantum information tasks, including cryptography and communication. However, unavoidable interactions between a system and its environment can degrade or even completely destroy measurement incompatibility; such a process is referred to as a measurement-incompatibility-annihilating channel. Recently, the capability of noisy quantum dynamics to preserve measurement incompatibility has been characterized within the resource theory of measurement incompatibility preservability. This motivates studying how to purify the preservation of measurement incompatibility and how to activate it from a measurement-incompatibility-annihilating channel. To this end, we first introduce our figures of merit as robustness-based resource monotones within this resource theory. We demonstrate that while pre-filtering operations can strengthen measurement incompatibility preservability, they cannot activate it from an incompatibility-annihilating channel, establishing a no-go theorem. Furthermore, we explicitly demonstrate that an incompatibility-annihilating channel can be stochastically activated via post-filtering operations. Our results provide a practical framework for exploiting measurement incompatibility in quantum information processing.
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