Robustness of random-control quantum-state tomography

Jingcheng Wang, Shaoliang Zhang, Jianming Cai, Zhenyu Liao, Christian Arenz, Ralf Betzholz

Research output: Contribution to journalArticlepeer-review

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)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.

Original languageEnglish (US)
Article number022408
JournalPhysical Review A
Volume108
Issue number2
DOIs
StatePublished - Aug 2023
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Fingerprint

Dive into the research topics of 'Robustness of random-control quantum-state tomography'. Together they form a unique fingerprint.

Cite this