Important progress in the research of quantum measurement characterization in the School of Modern Engineering, Nanjing University

Quantum measurement translates macroscopic quantum state information into classical events in detector response and is a bridge between the quantum world and the classical world. Accurate and efficient characterization of quantum measurements is an important prerequisite for extracting information about quantum systems, studying the fundamental theory of quantum physics, developing advanced quantum technologies, and realizing quantum superiority. The traditional method for characterizing quantum measurements is quantum detector lamination, which requires preparing a set of incident states with complete information and probing them with unknown quantum measurements, and reconstructing the measurement operators of quantum measurements using optimization algorithms according to the measurement results of different incident states. Although quantum detector lamination is theoretically universal for the characterization of arbitrary quantum measurements, however, the complexity of both the preparation process of the complete incident state and the reconstruction process of the measurement operator increases substantially as the dimensionality of the measurement operator increases, which poses a great challenge for the practical characterization of high-dimensional quantum measurements.

Recently, the School of Modern Engineering and Applied Science of Nanjing University, in collaboration with Zhijiang Laboratory, has presented a research result on the direct characterization of quantum measurements using weak values. This work takes advantage of the two-state vector description of quantum systems with temporal symmetry to perform weak measurements of pre- and post-selected quantum systems, establishes the correspondence between the generalized measurement results-weak values-and the quantum measurement operators that realize the post-selection process, and realizes the direct characterization of quantum measurements by extracting the weak values of different observable measurements, which is called direct quantum detector tomography (DQDT). Direct Quantum Detector Tomography (DQDT). In the experiments, the method is applied to the direct characterization of the projection measurements of the polarization degrees of freedom and the symmetry information-complete positive value operator measurements (SIC POVM), and the fidelity of the obtained measurement operators and the corresponding conventional quantum detector tomography results are greater than 99.5%. In addition, this work systematically investigates the accuracy of the direct lamination scheme and improves the accuracy of the direct characterization of the measurement operators by varying the coupling strength between the quantum system and the measurement instrument states and optimally utilizing the completeness conditions of the quantum measurement operators, making the direct quantum detector lamination universally feasible for characterizing arbitrary quantum measurements. This work extends the theory of direct quantum lamination based on weak values from quantum states and quantum processes to the characterization of quantum measurements, providing a new idea for the theoretical study of weak measurements in time-symmetric form, while the method circumvents the reconstruction process in traditional characterization methods, substantially reduces the computational complexity, and opens a new door for characterizing high-dimensional quantum measurements and studying the nonclassical nature of quantum measurements.

Figure 1. Diagram of the experimental setup for polarization projection measurements and direct characterization of SIC POVM using direct quantum detector lamination.

Figure 2. Experimental results (a, b) and accuracy analysis (c, d) of direct characterization of polarization projection measurements; (e) fidelity of direct characterization results versus conventional characterization results.

Figure 3. Experimental results (a, b, c) with accuracy analysis (d, e) for direct characterization of the polarization degree of freedom SIC POVM.

The above results were published in Physical Review Letters [DOI: 10.1103/PhysRevLett.127.180401] under the title "Direct Characterization of Quantum Measurements Using Weak Values".

The first author of the paper is Liang Xu, a research assistant in the School of Modern Engineering and Applied Science and a postdoctoral fellow in Zhijiang Laboratory, Nanjing University, and the corresponding author is Prof. Lijian Zhang, and Nanjing University is the first institution of the paper.

This work was supported by the National Key Research and Development Program of China (Grant No. 2017YFA0303703 and No. 2018YFA0306202), the National Natural Science Foundation of China (Grants No. 91836303, No. 61975077, No. 61490711, and No. 11690032), the Central University The Fundamental Research Funds of Central Universities (Grant No. 020214380068) supported this work.

Paper Link: https://mp.weixin.qq.com/s/IYlDJe7I4o7GuwJRDC__vA