我们引入一种单调度量来量化任意量子态中的非稳定子性（或简称魔法）。该单调量为纯态和混合态魔法的检测提供了充要判据。该单调量基于确定 Pauli 字符串期望值空间中稳定子多面体的边界。这些边界可由一组超平面不等式描述，其中违反任一不等式即为魔法的充要条件。该单调量通过寻找具有最大违反程度的超平面来构造，属于一种 Minkowski 泛函。我们还引入了一种基于类似方法的见证。由于待优化参数数量较少且具有离散性，该方法比现有的鲁棒魔法等忠实混合态单调量具有更高的计算效率。
英文摘要：
We introduce a monotone to quantify the amount of non-stabilizerness (or magic for short), in an arbitrary quantum state. The monotone gives a necessary and sufficient criterion for detecting the presence of magic for both pure and mixed states. The monotone is based on determining the boundaries of the stabilizer polytope in the space of Pauli string expectation values. The boundaries can be described by a set of hyperplane inequations, where violation of any one of these gives a necessary and sufficient condition for magic. The monotone is constructed by finding the hyperplane with the maximum violation and is a type of Minkowski functional. We also introduce a witness based on similar methods. The approach is more computationally efficient than existing faithful mixed state monotones such as robustness of magic due to the smaller number and discrete nature of the parameters to be optimized.
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Center for Quantum Science and Engineering, EPFL（洛桑联邦理工学院量子科学与工程中心）；International School for Advanced Studies (SISSA)（国际高等研究院）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）
Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
Scuola Superiore Meridionale（南方高等学院）；INFN Sezione di Napoli（那不勒斯 INFN 分部）；SISSA（的里雅斯特国际高等研究学校）；INFN Sezione di Trieste（的里雅斯特 INFN 分部）；Dipartimento di Fisica ‘Ettore Pancini’, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学物理系）
Dismagicker: Unitary Gate for Non-Stabilizerness Reduction
Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构与量子控制教育部重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Hefei National Laboratory（合肥国家实验室）
Non-stabilizerness in quantum-enhanced metrological protocols
Jagiellonian University（雅盖隆大学）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Mark Kac Complex Systems Research Center, Jagiellonian University in Kraków（雅盖隆大学马克·卡克复杂系统研究中心）；Qilimanjaro Quantum Tech（基利马扎罗量子技术公司）；ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究所光子学科学研究所）
Scuola Superiore Meridionale（南方高等学院）；INFN, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Dipartimento di Fisica ‘Ettore Pancini’, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；NFN, Sezione di Napoli（那不勒斯国家核物理研究所）
An Algorithm for Estimating $α$-Stabilizer Rényi Entropies via Purity
Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol（量子工程博士培训中心，H.H.威尔斯物理实验室和电气与电子工程系，布里斯托大学）；H.H. Wills Physics Laboratory, University of Bristol（H.H.威尔斯物理实验室，布里斯托大学）
Magic Steady State Production: Non-Hermitian, Dissipative, and Stochastic Pathways
University of Luxembourg（卢森堡大学）；Technical University of Munich, TUM School of Natural Sciences, Physics Department（慕尼黑工业大学自然科学学院物理系）；Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften（瓦尔特·迈斯纳研究所，巴伐利亚科学院）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
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）
Classical Simulations of Low Magic Quantum Dynamics
Rutgers University（罗格斯大学）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学）；Flatiron Institute（平顿研究所）
Complexity of frustration: a new source of non-local non-stabilizerness
Ruđer Bošković Institute（鲁德·博什科维奇研究所）；QOLS, Blackett Laboratory, Imperial College London（帝国理工学院布莱克特实验室量子光学与激光科学组）；Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学埃托雷·潘奇尼物理系）；Physics Department, University of Massachusetts Boston（马萨诸塞大学波士顿分校物理系）；INFN, Sezione di Napoli（意大利国家核物理研究院那不勒斯分部）
Experimental demonstration of non-local magic in a superconducting quantum processor
Università degli Studi di Napoli “Federico II”（那不勒斯费德里科二世大学）；Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN)（意大利国家核物理研究所）
School of Physics, Peking University（北京大学物理学院）；Department of Physics, Virginia Tech（弗吉尼亚理工大学物理系）；Center for High Energy Physics, Peking University（北京大学高能物理中心）
Van Hove singularities in stabilizer entropy densities
Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）
