Imaginarity-free quantum multiparameter estimation

Jisho Miyazaki1 and Keiji Matsumoto2

1Shinpouin, Mikataharacho, Kita-ku, Hamamatsu, Shizuoka, 433-8105, Japan
2Quantum Computation Group, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430

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Abstract

Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated until you discover the optimal measurement. Third, the optimal measurement may generally depend on the target values of parameters, and thus may be impossible to perform for unknown target states.
We present a method to circumvent these three obstacles. A class of quantum statistical models, which utilizes antiunitary symmetries or, equivalently, real density matrices, offers compatible multiparameter estimations. The symmetries accompany the target-independent optimal measurements for pure-state models. Based on this finding, we propose methods to implement antiunitary symmetries for quantum metrology schemes. We further introduce a function which measures antiunitary asymmetry of quantum statistical models as a potential tool to characterize quantumness of phase transitions.

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Cited by

[1] Yink Loong Len, "Multiparameter estimation for qubit states with collective measurements: a case study", New Journal of Physics 24 3, 033037 (2022).

[2] Francisco Delgado, "Symmetries of Quantum Fisher Information as Parameter Estimator for Pauli Channels under Indefinite Causal Order", Symmetry 14 9, 1813 (2022).

[3] Lijun Peng and Xiao-Ming Lu, "Generalization of Rayleigh's criterion on parameter estimation with incoherent sources", Physical Review A 103 4, 042601 (2021).

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