Enhanced parameter estimation by measurement of non-Hermitian operators
Abstract Quantum metrology aims at delivering new quantum-mechanical improvement to technologies of parameter estimations with precision bounded by the quantum Cramér-Rao bound. The currently used quantum Cramér-Rao bound was established with measurements of observables restricted to be Hermitian. T...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer
2023-10-01
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| Series: | AAPPS Bulletin |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/s43673-023-00089-0 |
| _version_ | 1797557532664791040 |
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| author | Jianning Li Haodi Liu Zhihai Wang X. X. Yi |
| author_facet | Jianning Li Haodi Liu Zhihai Wang X. X. Yi |
| author_sort | Jianning Li |
| collection | DOAJ |
| description | Abstract Quantum metrology aims at delivering new quantum-mechanical improvement to technologies of parameter estimations with precision bounded by the quantum Cramér-Rao bound. The currently used quantum Cramér-Rao bound was established with measurements of observables restricted to be Hermitian. This constrains the bound and limits the precision of parameter estimation. In this paper, we lift the constraint and derive a previously unknown quantum Cramér-Rao bound. We find that the new bound can reach arbitrary small value with mixed states and it breaks the Heisenberg limit in some cases. We construct a setup to measure non-Hermitian operators and discuss the saturation of the present bound. Two examples—the phase estimation with Greenberger-Horne-Zeilinger states of trapped ions and the adiabatic quantum parameter estimation with the nuclear magnetic resonance—are employed to demonstrate the theory. The present study might open a new research direction—non-Hermitian quantum metrology. |
| first_indexed | 2024-03-10T17:18:17Z |
| format | Article |
| id | doaj.art-703742b0c5d3463e9e1d8be33cbd6bcb |
| institution | Directory Open Access Journal |
| issn | 2309-4710 |
| language | English |
| last_indexed | 2024-03-10T17:18:17Z |
| publishDate | 2023-10-01 |
| publisher | Springer |
| record_format | Article |
| series | AAPPS Bulletin |
| spelling | doaj.art-703742b0c5d3463e9e1d8be33cbd6bcb2023-11-20T10:26:07ZengSpringerAAPPS Bulletin2309-47102023-10-0133111010.1007/s43673-023-00089-0Enhanced parameter estimation by measurement of non-Hermitian operatorsJianning Li0Haodi Liu1Zhihai Wang2X. X. Yi3Center for Quantum Sciences and School of Physics, Northeast Normal UniversityCenter for Quantum Sciences and School of Physics, Northeast Normal UniversityCenter for Quantum Sciences and School of Physics, Northeast Normal UniversityCenter for Quantum Sciences and School of Physics, Northeast Normal UniversityAbstract Quantum metrology aims at delivering new quantum-mechanical improvement to technologies of parameter estimations with precision bounded by the quantum Cramér-Rao bound. The currently used quantum Cramér-Rao bound was established with measurements of observables restricted to be Hermitian. This constrains the bound and limits the precision of parameter estimation. In this paper, we lift the constraint and derive a previously unknown quantum Cramér-Rao bound. We find that the new bound can reach arbitrary small value with mixed states and it breaks the Heisenberg limit in some cases. We construct a setup to measure non-Hermitian operators and discuss the saturation of the present bound. Two examples—the phase estimation with Greenberger-Horne-Zeilinger states of trapped ions and the adiabatic quantum parameter estimation with the nuclear magnetic resonance—are employed to demonstrate the theory. The present study might open a new research direction—non-Hermitian quantum metrology.https://doi.org/10.1007/s43673-023-00089-0Parameter estimationQuantum metrologyNon-Hermitian operatorsQuantum Cramér-Rao bound |
| spellingShingle | Jianning Li Haodi Liu Zhihai Wang X. X. Yi Enhanced parameter estimation by measurement of non-Hermitian operators AAPPS Bulletin Parameter estimation Quantum metrology Non-Hermitian operators Quantum Cramér-Rao bound |
| title | Enhanced parameter estimation by measurement of non-Hermitian operators |
| title_full | Enhanced parameter estimation by measurement of non-Hermitian operators |
| title_fullStr | Enhanced parameter estimation by measurement of non-Hermitian operators |
| title_full_unstemmed | Enhanced parameter estimation by measurement of non-Hermitian operators |
| title_short | Enhanced parameter estimation by measurement of non-Hermitian operators |
| title_sort | enhanced parameter estimation by measurement of non hermitian operators |
| topic | Parameter estimation Quantum metrology Non-Hermitian operators Quantum Cramér-Rao bound |
| url | https://doi.org/10.1007/s43673-023-00089-0 |
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