The relation between projective measurements and generalized quantum measurements is a fundamental problem in quantum physics, and clarifying this issue is also important to quantum technologies. While it has been intuitively known that projective measurements can be constructed from sequential generalized or weak measurements [1, 2], there is still lack of a proof of this hypothesis in general cases. Here we prove it from the perspective of quantum channels . We show that projective measurements naturally arise from sequential generalized measurements in the asymptotic limit. Specifically, a selective projective measurement arises from a set of typical sequences of sequential generalized measurements. We provide an explicit scheme to construct projective measurements of a quantum system with sequential generalized quantum measurements. Remarkably, a single ancilla qubit is sufficient to mediate sequential generalized measurements for constructing arbitrary projective measurements of a generic system, which can have applications in readout, initialization, and feedback control of a quantum system. As an example, we present a protocol to measure the modular excitation numbers of a bosonic mode with an ancilla qubit, which are exactly the error syndromes of rotation-symmetric bosonic quantum error correction codes.
- Wen-Long Ma, Ping Wang, Weng-Hang Leong, Ren-Bao Liu*, Phys. Rev. A 98, 012117 (2018).
- Gang-Qin Liu, Jian Xing, Wen-Long Ma, Ping Wang, Chang-Hao Li, Hoi Chun Po, Yu-Ran Zhang, Heng Fan, Ren-Bao Liu, Xinyu Pan*, Phys. Rev. Lett. 118, 150504 (2017).
- Wen-Long Ma*, Shu-Shen Li, Ren-Bao Liu, Phys. Rev. A 107, 012217 (2023).
马稳龙，现为中国科学院半导体所研究员、博士生导师，中国科学院大学岗位教授。2015年在中科院半导体所获得博士学位，2015年2020年先后在香港中文大学、耶鲁大学和芝加哥大学从事博士后研究, 随后加入中科院半导体所超晶格国家重点实验室，并入选国家高层次人才引进计划青年项目。研究领域为固态量子信息理论，在量子退相干、量子控制、量子纠错和量子测量等领域取得了一系列创新成果，在包括PRL的PR系列, Nature Physics, Nature Communications等期刊上发表文章二十余篇。