A generic qubit unitary operator affected by depolarizing noise is duplicated and inserted in a quantum switch process realizing a superposition of causal orders. The characterization of the resulting switched quantum channel is worked out for its action on the joint state of the probe-control qubit pair. The switched channel is then specifically investigated for the important metrological task of phase estimation on the noisy unitary operator, with the performance assessed by the Fisher information, classical or quantum. A comparison is made with conventional techniques of estimation where the noisy unitary is directly probed in a one-stage or two-stage cascade with definite order, or several uses of them with two or more qubits. In the switched channel with indefinite order, specific properties are reported, meaningful for estimation and not present with conventional techniques. It is shown that the control qubit, although it never directly interacts with the unitary, can nevertheless be measured alone for effective estimation, while discarding the probe qubit that interacts with the unitary. Also, measurement of the control qubit maintains the possibility of efficient estimation in difficult conditions where conventional estimation becomes less efficient, as with ill-configured input probes, or in blind situations when the axis of the unitary is unknown. Effective estimation by measuring the control qubit remains possible even when the input probe tends to align with the axis of the unitary, or with a fully depolarized input probe, while in these conditions conventional estimation gets inoperative. Measurement of the probe qubit of the switched channel is also shown to add useful capabilities for phase estimation. The results contribute to the analysis of switched quantum channels with indefinite order for information processing, and uncover new possibilities for qubit metrology.
Scaling Enhancement in Quantum Metrology via Indefinite-Time-Direction Encoding
Shanghai Jiao Tong University（上海交通大学）；The University of Hong Kong（香港大学）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）
Quantum time-flip beats adaptive metrology: Asymptotic benefit, activation, and unsimulability
Indian Institute of Science Education and Research（印度科学教育与研究所）；Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Networked Quantum Devices Unit, Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学量子设备网络单元）；Université Paris-Saclay（巴黎萨克雷大学）
Quantum metrology enhanced by effective time reversal
Joint Center for Quantum Information and Computer Science, NIST and University of Maryland（马里兰大学量子信息与计算联合中心）；University of Cambridge（剑桥大学）；Hitachi Cambridge Laboratory（日立剑桥实验室）；Department of Electrical Engineering and Computer Science（加州大学伯克利分校电气工程和计算机科学系）；University of California, Berkeley（加州大学伯克利分校物理系）；Department of Physics, University of California, Berkeley（马里兰大学物理科学与技术研究所）；Institute for Physical Science and Technology, University of Maryland
Journey in quantum metrology and sensing from foundations to applications: a review
Harish-Chandra Research Institute（哈里什-钱德拉研究所）；Homi Bhabha National Institute（霍米·巴哈国家研究所）；Instytut Fizyki Teoretycznej, Wydział Fizyki, Astronomii i Informatyki Stosowanej, Uniwersytet Jagielloński（雅盖隆大学物理、天文学与应用信息学系理论物理研究所）
Optimal Strategies for Multi-parameter Quantum Metrology
The Chinese University of Hong Kong（香港中文大学）；The University of Hong Kong（香港大学）；The Hong Kong Institute of Quantum Information Science and Technology（香港量子信息科学与技术研究所）
