Imaginarity-free quantum multiparameter estimation

Jisho Miyazaki; Keiji Matsumoto

doi:10.22331/q-2022-03-10-665

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

Published:	2022-03-10, volume 6, page 665
Eprint:	arXiv:2010.15465v3
Doi:	https://doi.org/10.22331/q-2022-03-10-665
Citation:	Quantum 6, 665 (2022).

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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.

► BibTeX data

@article{Miyazaki2022imaginarityfree,
  doi = {10.22331/q-2022-03-10-665},
  url = {https://doi.org/10.22331/q-2022-03-10-665},
  title = {Imaginarity-free quantum multiparameter estimation},
  author = {Miyazaki, Jisho and Matsumoto, Keiji},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {665},
  month = mar,
  year = {2022}
}

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