Robustness of random-control quantum-state tomography

• URL: http://arxiv.org/abs/2302.07439v2
• Date: Thu, 10 Aug 2023 05:14:35 GMT
• Title: Robustness of random-control quantum-state tomography
• Authors: Jingcheng Wang, Shaoliang Zhang, Jianming Cai, Zhenyu Liao, Christian Arenz, and Ralf Betzholz
• Abstract summary: We analyze the robustness of a recently demonstrated quantum-state tomography scheme against measurement errors. We also perform numerical simulations to investigate the temporal behavior of the robustness for two specific quantum systems driven by a single random control field.
• Score: 5.169507714267699
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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