Robustness of random-control quantum-state tomography
Robustness of random-control quantum-state tomography
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DOI：
10.1103/physreva.108.022408
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发表时间：
2023-02
影响因子：
2.9
通讯作者：
Jingcheng Wang;Shaoliang Zhang;J. Cai;Zhenyu Liao;C. Arenz;R. Betzholz
中科院分区：
文献类型：
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作者：
Jingcheng Wang;Shaoliang Zhang;J. Cai;Zhenyu Liao;C. Arenz;R. Betzholz
在最近演示的量子态层析成像方案中[Phys.莱特牧师。124,010405(2020年)]，将随机控制场局部应用于多体系统，通过单能观测量重建系统的全量子态。在这里，我们分析了这种层析成像方案对测量误差的稳健性。我们使用完全描述层析成像过程的线性系统的条件数的对数来表征对测量误差的敏感性。利用随机矩阵理论的结果，当考虑Haar-随机演化时，我们得到了条件数关于系统规模的对数的标度律。虽然这个表达式与Haar随机性的产生方式无关，但我们也进行了数值模拟来研究由单个随机控制场驱动的两个特定量子系统的健壮性的时间行为。有趣的是，我们发现，在作为驱动时间函数的条件数的对数的平均值渐近于Haar-随机演化的预测值之前，它达到了一个平台，其长度随着系统的大小而增加。
In a recently demonstrated quantum-state tomography scheme [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 logarithm of 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 on 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.