CIF: Small: Resource Theories of Quantum Channels

量子信息科学以“纠缠”科学为基础，即两个或两个以上物体的量子态必须相互参照来描述，即使单个物体在空间上是分开的。尽管在近一个世纪前就被发现了，但关于量子系统中资源与可以实现的纠缠水平之间的关系，人们还不太了解。本项目旨在回答量子通道纠缠资源理论中的一些基本问题。准备一个量子态或模拟一个量子通道需要多少纠缠？从这些相同的资源中可以提炼出多少纠缠？执行给定的量子计算需要多少“神奇量子态”？在量子信道上实现通信的量子优势需要多少“非高斯性”？两个量子态或通道的区别有多大？该项目解决的问题对量子信息处理的许多应用特别感兴趣，例如解决计算难题和实现安全和隐蔽通信。该项目还将通过广泛的教育和课程发展活动，培养这一领域的跨学科骨干学生。本项目将探讨量子通道资源理论的基础问题。量子资源理论的传统观点关注的是如何利用自由操作将一个有资源的量子态转换为另一个有资源的量子态。例如，纠缠理论中一个基本的众所周知的问题是确定二部态的可蒸馏纠缠，它等于通过使用局部操作和经典通信免费从给定二部态的许多副本中提取新的贝尔态的最大速率。这个研究项目的目的是将这类问题提升到一个新的水平，主要问题是：使用自由信道将一个资源丰富的量子信道转换为另一个资源丰富的量子信道的最佳方法是什么？该项目旨在确定量子通道的纠缠措施，以便在有效计算的同时解决上述问题，并了解其他资源理论中的动态过程，如魔法状态和通道、可区分性、纯度、热力学、非高斯性、该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，认为值得支持。

Quantum information science is based on the science of 'entanglement', where the quantum states of two or more objects have to be described with reference to each other, even though the individual objects are spatially separated. Despite being identified nearly a century ago, much is not understood regarding the relationship between the resources in a quantum system and the level of entanglement that can be achieved. This project seeks to answer some fundamental questions in the resource theory of entanglement for quantum channels. How much entanglement is required to prepare a quantum state or to simulate a quantum channel? How much entanglement can one distill from these same resources? How many "magic quantum states" are required to perform a given quantum computation? How much "non-Gaussianity" is required to achieve a quantum advantage in communication over quantum channels? How distinguishable are two quantum states or channels? The questions that this project addresses are of particular interest for the many applications of quantum information processing, such as solving computationally hard problems and enabling secure and covert communications. The project will also train an inter-disciplinary cadre of students in this domain through extensive education and curriculum development activities. This project will address foundational questions concerning resource theories of quantum channels. The traditional perspective in quantum resource theories concerns how to use free operations to convert one resourceful quantum state to another one. For example, a fundamental and well known question in entanglement theory is to determine the distillable entanglement of a bipartite state, which is equal to the maximum rate at which fresh Bell states can be distilled from many copies of a given bipartite state by employing local operations and classical communication for free. It is the aim of this research project to take this kind of question to the next level, with the main question being: What is the best way of using free channels to convert one resourceful quantum channel to another? The project seeks to identify measures of entanglement for quantum channels that allow for addressing the above questions while being efficiently computable, and also to understand dynamical processes in other resource theories, such as magic states and channels, distinguishability, purity, thermodynamics, non-Gaussianity, etc.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.