TY - JOUR
T1 - Robustness of random-control quantum-state tomography
AU - Wang, Jingcheng
AU - Zhang, Shaoliang
AU - Cai, Jianming
AU - Liao, Zhenyu
AU - Arenz, Christian
AU - Betzholz, Ralf
N1 - Publisher Copyright:
© 2023 American Physical Society.
PY - 2023/8
Y1 - 2023/8
N2 - 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)0031-900710.1103/PhysRevLett.124.010405], 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.
AB - 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)0031-900710.1103/PhysRevLett.124.010405], 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.
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U2 - 10.1103/PhysRevA.108.022408
DO - 10.1103/PhysRevA.108.022408
M3 - Article
AN - SCOPUS:85167873897
SN - 2469-9926
VL - 108
JO - Physical Review A
JF - Physical Review A
IS - 2
M1 - 022408
ER -