Direct Strong Measurement of a High-Dimensional Quantum State**Supported by the National Natural Science Foundation of China (Grant Nos. 11574291, 11774334, 11774335, 11674306 and 61590932), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB01030200), the National Key Research and Development Program of China (Grant Nos. 2016YFA0301300, 2016YFA0301700 and 2017YFA0304100), the Key Research Program of Frontier

Abstract

It is of great importance to determine an unknown quantum state for fundamental studies of quantum mechanics, yet it is still difficult to characterize systems of large dimensions in practice. Although the scan-free direct measurement approach based on a weak measurement scheme was proposed to measure a high-dimensional photonic state, how weak the interaction should be to give a correct estimation remains unclear. Here we propose and experimentally demonstrate a technique that measures a high-dimensional quantum state with the combination of scan-free measurement and direct strong measurement. The procedure involves sequential strong measurement, in which case no approximation is made similarly to the conventional direct weak measurement. We use this method to measure a transverse state of a photon with effective dimensionality of 65000 without the time-consumed scanning process. Furthermore, the high fidelity of the result and the simplicity of the experimental apparatus show that our approach can be readily used to measure the complex field of a beam in diverse applications such as wavefront sensing and quantitative phase imaging.