近日，华中科技大学的Ralf Betzholz及其研究小组与美国亚利桑那州立大学的Christian Arenz等人合作并取得一项新进展。经过不懈努力，他们证实随机控制量子态断层照相技术的鲁棒性。相关研究成果已于2023年8月9日在国际知名学术期刊《物理评论A》上发表。
该研究团队分析了断层照相方案对测量误差的鲁棒性。研究人员利用充分描述断层照相过程的线性系统的条件数来表征对测量误差的灵敏度。他们利用随机矩阵理论的结果，导出了考虑Haar-随机演化时，该条件数的对数对系统大小的定标律。虽然该表达式与Haar随机性如何生成无关，但研究人员也进行了数值模拟来研究由单次随机控制场驱动的两个特定量子系统的鲁棒性的时间行为。
有趣的是，他们发现，在条件数的对数平均值渐近接近haar随机演化的预测值之前，它先达到了一个高原，该高原的长度随着系统规模的增加而增加。
据悉，在最近展示的量子态断层照相方案中，随机控制场被局部应用于多粒子系统，以通过单次观测来测量并重建系统的全量子态。
附：英文原文
Title: Robustness of random-control quantum-state tomography
Author: Jingcheng Wang, Shaoliang Zhang, Jianming Cai, Zhenyu Liao, Christian Arenz, Ralf Betzholz
Issue&Volume: 2023/08/09
Abstract: In a recently demonstrated quantum-state tomography scheme [P. Yang, M. Yu, R. Betzholz, C. Arenz, and J. Cai, Phys. Rev. Lett. 124, 010405 (2020)], a random-control field is locally applied to a multipartite system to reconstruct the full quantum state of the system through single-observable measurements. Here, we analyze the robustness of such a tomography scheme against measurement errors. We characterize the sensitivity to measurement errors using the condition number of a linear system that fully describes the tomography process. Using results from random matrix theory we derive the scaling law of the logarithm of this condition number with respect to the system size when Haar-random evolutions are considered. While this expression is independent of how Haar randomness is created, we also perform numerical simulations to investigate the temporal behavior of the robustness for two specific quantum systems that are driven by a single random-control field. Interestingly, we find that before the mean value of the logarithm of the condition number as a function of the driving time asymptotically approaches the value predicted for a Haar-random evolution it reaches a plateau whose length increases with the system size.
DOI: 10.1103/PhysRevA.108.022408
Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.108.022408
来源：科学网 小柯机器人