On the regularization and optimization in quantum detector tomography

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Xiao, Shuixin
Wang, Yuanlong
Zhang, Jun
Dong, Daoyi
Yokoyama, Shota
Petersen, Ian R
Yonezawa, Hidehiro
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2023
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Abstract

Quantum detector tomography (QDT) is a fundamental technique for calibrating quantum devices and performing quantum engineering tasks. In this paper, we utilize regularization to improve the QDT accuracy whenever the probe states are informationally complete or informationally incomplete. In the informationally complete scenario, without regularization, we optimize the resource (probe state) distribution by converting it to a semidefinite programming problem. Then in both the informationally complete and informationally incomplete scenarios, we discuss different regularization forms and prove the mean squared error scales as O(1/N) or tends to a constant with N state copies under the static assumption. We also characterize the ideal best regularization for the identifiable parameters, accounting for both the informationally complete and informationally incomplete scenarios. Numerical examples demonstrate the effectiveness of different regularization forms and a quantum optical experiment test shows that a suitable regularization form can reach a reduced mean squared error.

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Automatica

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155

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© 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/

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Engineering

Information and computing sciences

Mathematical sciences

Science & Technology

Technology

Automation & Control Systems

Engineering, Electrical & Electronic

Engineering

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Xiao, S; Wang, Y; Zhang, J; Dong, D; Yokoyama, S; Petersen, IR; Yonezawa, H, On the regularization and optimization in quantum detector tomography, Automatica, 2023, 155, pp. 111124

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