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TMF, 2010, Volume 165, Number 2, Pages 370–384 (Mi tmf6583)  

This article is cited in 5 scientific papers (total in 5 papers)

Clocks and Fisher information

Ping Chena, Shunlong Luob

a Department of Economics, University of Melbourne, Melbourne, Australia
b Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, P. R. China

Abstract: In a broad sense, any parametric family of quantum states can be viewed as a quantum clock. The time, which is the parameter, is encoded in the corresponding quantum states. The quality of such a clock depends on how precisely we can distinguish the states or, equivalently, estimate the parameter. In view of the quantum Cramér–Rao inequalities, the quality of quantum clocks can be characterized by the quantum Fisher information. We address the issue of quantum clock synchronization in terms of quantum Fisher information and demonstrate its fundamental difference from the classical paradigm. The key point is the superadditivity of Fisher information, which always holds in the classical case but can be violated in quantum mechanics. The violation can occur for both pure and mixed states. Nevertheless, we establish the superadditivity of quantum Fisher information for any classical–quantum state. We also demonstrate an alternative form of superadditivity and propose a weak form of superadditivity. The violation of superadditivity can be exploited to enhance quantum clock synchronization.

Keywords: Fisher information, quantum estimation, superadditivity, classical–quantum state, clock synchronization

DOI: https://doi.org/10.4213/tmf6583

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English version:
Theoretical and Mathematical Physics, 2010, 165:2, 1552–1564

Bibliographic databases:

Document Type: Article
Received: 03.02.2010
Revised: 01.03.2010

Citation: Ping Chen, Shunlong Luo, “Clocks and Fisher information”, TMF, 165:2 (2010), 370–384; Theoret. and Math. Phys., 165:2 (2010), 1552–1564

Citation in format AMSBIB
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\by Ping~Chen, Shunlong~Luo
\paper Clocks and Fisher information
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\vol 165
\issue 2
\pages 370--384
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\crossref{https://doi.org/10.4213/tmf6583}
\transl
\jour Theoret. and Math. Phys.
\yr 2010
\vol 165
\issue 2
\pages 1552--1564
\crossref{https://doi.org/10.1007/s11232-010-0129-9}
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  • http://mi.mathnet.ru/eng/tmf/v165/i2/p370

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Lu X.-M., Sun Zh., Wang X., Luo Sh., Oh C.H., “Broadcasting Quantum Fisher Information”, Phys. Rev. A, 87:5 (2013), 050302  crossref  isi  elib  scopus
    2. Song H., Luo Sh., Li N., Chang L., “Comparing Quantum Cloning: a Fisher-Information Perspective”, Phys. Rev. A, 88:4 (2013), 042121  crossref  mathscinet  adsnasa  isi  elib  scopus
    3. Chang L., Li N., Luo Sh., Song H., “Optimal Extraction of Information From Two Spins”, Phys. Rev. A, 89:4 (2014), 042110  crossref  adsnasa  isi  scopus
    4. Song H., Luo Sh., Fu Sh., “Quantum criticality from Fisher information”, Quantum Inf. Process., 16:4 (2017), UNSP 91  crossref  mathscinet  isi  scopus
    5. Kwon H., Jeong H., Jennings D., Yadin B., Kim M.S., “Clock-Work Trade-Off Relation For Coherence in Quantum Thermodynamics”, Phys. Rev. Lett., 120:15 (2018), 150602  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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