Xu Liang, Xu Huichao, Jiang Tao, Xu Feixiang, Zheng Kaimin, Wang Ben, Zhang Aonan, Zhang Lijian
National Laboratory of Solid State Microstructures, Key Laboratory of Intelligent Optical Sensing and Manipulation, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.
Research Center for Quantum Sensing, Zhejiang Lab, Hangzhou 310000, China.
Phys Rev Lett. 2021 Oct 29;127(18):180401. doi: 10.1103/PhysRevLett.127.180401.
The time-symmetric formalism endows the weak measurement and its outcome, the weak value, with many unique features. In particular, it allows a direct tomography of quantum states without resorting to complicated reconstruction algorithms and provides an operational meaning to wave functions and density matrices. Here, we propose and experimentally demonstrate the direct tomography of a measurement apparatus by taking the backward direction of weak measurement formalism. Our protocol works rigorously with the arbitrary measurement strength, which offers improved accuracy and precision. The precision can be further improved by taking into account the completeness condition of the measurement operators, which also ensures the feasibility of our protocol for the characterization of the arbitrary quantum measurement. Our work provides new insight on the symmetry between quantum states and measurements, as well as an efficient method to characterize a measurement apparatus.
时间对称形式体系赋予弱测量及其结果（即弱值）许多独特特性。特别是，它允许直接对量子态进行层析成像，而无需借助复杂的重构算法，并为波函数和密度矩阵提供了可操作的意义。在此，我们通过采用弱测量形式体系的反向过程，提出并通过实验证明了对测量装置的直接层析成像。我们的方案在任意测量强度下都能严格起作用，从而提高了准确性和精度。通过考虑测量算子的完备性条件，精度可以进一步提高，这也确保了我们的方案用于表征任意量子测量的可行性。我们的工作为量子态与测量之间的对称性提供了新的见解，以及一种表征测量装置的有效方法。
