钻石范数和相关测度在量子映射非物理性量化中的应用
Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
摘要：
虽然量子信道是量子态动力学的基础，但在纠缠检测、非马尔可夫量子动力学或错误缓解等环境中，经常会遇到不是物理信道的映射--也就是说，不是完全正的映射。我们介绍了一种操作方法的非物理性的定量研究的线性映射的基础上，不同的方式来近似一个给定的线性映射与量子信道。我们的第一个措施直接量化的成本模拟一个给定的地图使用物理上可实现的量子信道，转移到模拟量子态的线性组合的任务，模拟非物理动力学的困难。我们的第二个衡量基准的量化优势，一个非完全积极的地图可以提供基于歧视的量子游戏。值得注意的是，我们表明，对于任何保迹映射，数量都减少到一个基本的距离测度：钻石规范，从而赋予这个规范与新的操作意义的线性映射的特征。我们讨论了我们的结果的应用程序，结构物理近似的正映射，量化的非马尔可夫性，并限制错误缓解的成本。
英文摘要：
Although quantum channels underlie the dynamics of quantum states, maps which are not physical channels -- that is, not completely positive -- can often be encountered in settings such as entanglement detection, non-Markovian quantum dynamics, or error mitigation. We introduce an operational approach to the quantitative study of the non-physicality of linear maps based on different ways to approximate a given linear map with quantum channels. Our first measure directly quantifies the cost of simulating a given map using physically implementable quantum channels, shifting the difficulty in simulating unphysical dynamics onto the task of simulating linear combinations of quantum states. Our second measure benchmarks the quantitative advantages that a non-completely-positive map can provide in discrimination-based quantum games. Notably, we show that for any trace-preserving map, the quantities both reduce to a fundamental distance measure: the diamond norm, thus endowing this norm with new operational meanings in the characterisation of linear maps. We discuss applications of our results to structural physical approximations of positive maps, quantification of non-Markovianity, and bounding the cost of error mitigation.
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