The accuracy of the Arthurs-Kelly model of a simultaneous measurement of position and momentum is analysed using concepts developed by Braginsky and Khalili in the context of measurements of a single quantum observable. A distinction is made between the errors of retrodiction and prediction. It is shown that the distribution of measured values coincides with the initial state Husimi function when the retrodictive accuracy is maximised, and that it is related to the final state anti-Husimi function (the P representation of quantum optics) when the predictive accuracy is maximised. The disturbance of the system by the measurement is also discussed. A class of minimally disturbing measurements is characterised. It is shown that the distribution of measured values then coincides with one of the smoothed Wigner functions described by Cartwright.
Effects of the free evolution in the Arthurs-Kelly model of simultaneous measurement and in the retrodictive predictions of the Heisenberg uncertainty relations
Time-of-arrival distributions from position-momentum and energy-time joint measurements
从Arthurs和Kelly联合测量模型获得的位置-动量准分布被用于按照Kochaubrski和Wódkiewicz提出的量化程序间接获得“操作”到达时间（TOA）分布[Phys. Rev. A 60，2689（1999）]。该TOA分布不是时间协变的。通过使用其他相空间准分布的过程是广义的，并提供充分条件的时间协方差，限制可能的相空间准分布基本上维格纳函数，然而，提供了一个非正的TOA准分布。这些问题用另一方面不保证归一化的不同量化过程来补救。最后，Arthurs和Kelly测量模型的TOA和能量（有效的任意共轭变量时，其中一个变量是有界的从下面）的工作。这样得到的边际TOA分布是Kijowski分布的扭曲版本，是时间协变的、正的和归一化的。
Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation
The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Institute of Quantum Information Science and Technology（香港量子信息科学与技术研究所）；State Key Laboratory of Quantum Information Technologies and Materials（量子信息技术与材料国家重点实验室）；Shenzhen University（深圳大学）
Tight tradeoff relation and optimal measurement for multiparameter quantum estimation
The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Institute of Quantum Information Science and Technology, The Chinese University of Hong Kong（香港中文大学香港量子信息科学与技术研究所）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）；Shenzhen University（深圳大学）
