The manipulation of quantum "resources" such as entanglement, coherence and magic states lies at the heart of quantum science and technology, empowering potential advantages over classical methods. In practice, a particularly important kind of manipulation is to "purify" the quantum resources, since they are inevitably contaminated by noise and thus often lose their power or become unreliable for direct usage. Here we prove fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource. More explicitly, we derive nontrivial lower bounds on the error of converting any full-rank noisy state to any target pure resource state by any free protocol (including probabilistic ones)---it is impossible to achieve perfect resource purification, even probabilistically. Our theorems indicate strong limits on the efficiency of distillation, a widely used type of resource purification routine that underpins many key applications of quantum information science. In particular, this general result induces the first explicit lower bounds on the resource cost of magic state distillation, a leading scheme for realizing scalable fault-tolerant quantum computation. Implications for the standard error-correction-based methods are specifically discussed.
No-go theorems for quantum resource purification II: new approach and channel theory
最近已经表明，从噪声资源状态到纯资源状态的转换的准确性和效率存在普遍的基本限制（例如，~蒸馏）在任何表现良好的量子资源理论中[Fang/Liu，Phys. Rev. Lett. 125，060405（2020）]。在这里，我们开发了一种新的和强大的方法来分析量子资源纯化的限制，这不仅导致改进的边界，排除了更广泛的噪声状态的精确纯化，并在某些情况下是紧的，但也使我们能够建立一个强大的量子信道（动态）资源不纯化理论。更具体地说，我们采用新的方法来获得通用的边界上的错误和成本的转换通用噪声信道（其中多个实例可以自适应地使用，与状态理论相比），一些单一的资源信道下的任何自由信道到信道映射。我们解决几个案件的实际利益更具体的条款，并讨论了我们的一般结果蒸馏，量子纠错，量子香农理论和量子线路合成的连接和应用。
Forward-Assisted Purification: A Spatiotemporal Framework Beyond Conventional Limits
School of Physics and Astronomy, University of Glasgow（格拉斯哥大学物理与天文学学院）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局高性能计算研究所）
Universal quantum state purification under energy-preserving constraints
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；South China University of Technology（华南理工大学）；The University of Hong Kong（香港大学）
Non-local Magic: closed-form solution and equivalence with magic of purification
Università degli Studi di Salerno（萨莱诺大学）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）；Scuola Superiore Meridionale（南方高等学院）；Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）
Enhancing the teleportation fidelity of a quantum network using purification
Centre for Quantum Science and Technology, International Institute of Information Technology, Hyderabad（海得拉巴国际信息研究院量子科学与技术中心）；Department of Physics and Center of excellence in Quantum information, computation, science and technology, Indian Institute of Technology Bombay（孟买印度理工学院物理系及量子信息、计算、科学与技术卓越中心）；Center for Security, Theory and Algorithmic Research, International Institute of Information Technology, Hyderabad（海得拉巴国际信息研究院安全、理论与算法研究中心）
Photon-efficient quantum repeater chains via hyperentanglement-assisted purification
University of Pisa（比萨大学）；Institute for Informatics and Telematics (IIT), National Research Council (CNR)（意大利国家研究委员会信息与遥测研究所）；Department of Physics, University of Naples Federico II（那不勒斯费德里科二世大学物理系）；National Institute of Optics (INO), National Research Council (CNR)（意大利国家研究委员会光学国家研究所）
Nearly Optimal T-Count for Symmetry-Based Quantum State Purification
State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所处理器重点实验室）；School of Computer Science and Technology, University of Chinese Academy of Sciences（中国科学院大学计算机科学与技术学院）；Shandong University（山东大学）；Thrust of Artificial Intelligence, Information Hub, The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州）信息枢纽人工智能领域）
Distilling Qubit Unitary Operations: A No-Go Theorem and Minimal Realization
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Record Loss Sets a Rare-Trajectory Limit on Quantum Purification
School of Instrumentation and Optoelectronic Engineering, Beihang University（北京航空航天大学仪器科学与光电工程学院）；Institute of Large-Scale Scientific Facility, Beihang University（北京航空航天大学大型科学装置研究院）；Hangzhou Institute of Extremely-Weak Magnetic Field Major National Science and Technology Infrastructure（杭州极弱磁场重大科技基础设施研究院）；Hangzhou Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）
