We address the discontinuities of the quantum Fisher information (QFI) that may arise when the parameter of interest takes values that change the rank of the quantum statistical model. We revisit the classical and the quantum Cramér-Rao theorems, show that they do not hold in these limiting cases, and discuss how this impacts on the relationship between the QFI and the Bures metric. In order to illustrate the metrological implications of our findings, we present two paradigmatic examples, where we discuss in detail the role of the discontinuities and show that the Cramér-Rao may be easily violated.
Extremal properties of the variance and the quantum Fisher information
我们表明，方差是自己的凹屋顶。对于秩为2的密度矩阵和密度矩阵的本征基中对角元素为零的算子，我们解析地证明了量子费舍尔信息是方差凸屋顶的4倍。强有力的数值证据表明，这一说法是真实的，甚至对运营商与非零对角元素或密度矩阵的秩大于2。我们还发现，在[D. Petz，J.Phys.A：Math.Gen.35，929（2002）; P. Gibilisco，F. Hiai和D. Petz，IEEE Trans. Inf. Theory 55，439（2009）]，在适当的归一化之后，量子费舍尔信息是最大的。因此，我们推测，即使在一般情况下，量子费舍尔信息也是方差凸屋顶的四倍。
Entanglement depth and ancilla efficiency in quantum channel estimation
Palacký University（帕拉茨基大学）；Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS（帕拉茨基大学与捷克科学院物理研究所联合光学实验室）；Institute of Physics of CAS（捷克科学院物理研究所）
Quantum Fisher Information as the Speed Limit for Multipartite Entanglement
Argonne National Laboratory（阿贡国家实验室）；Stevens Institute of Technology（史蒂文斯理工学院）；Southern Illinois University（南伊利诺伊大学）；Center for Nanoscale Materials, Argonne National Laboratory（阿贡国家实验室纳米材料中心）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究 institute 特里凡得琅）
Deciding the Attainability of the Multiparameter Quantum Fisher Information is NP-Hard
Joint Quantum Institute, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学联合量子研究所）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学量子信息与计算科学联合中心）；Centre for Quantum Technologies (CQT), National University of Singapore（新加坡国立大学量子技术中心）；Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（科学技术研究局量子创新中心）；UMIACS, University of Maryland（马里兰大学计算机科学与信息系统多学科研究中心）；Center for Quantum Software and Innovation, University of Technology Sydney（悉尼科技大学量子软件与创新中心）；Department of Quantum Science and Technology, Research School of Physics, The Australian National University（澳大利亚国立大学物理研究学院量子科学与技术系）；Axiomatic AI, Inc.（公理人工智能公司）；Graduate School of Informatics and Engineering, The University of Electro-Communications（电气通信大学信息工程学研究生院）
