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Cited by 163Quantum Information and CryptographyQuantum Computing Algorithms and ArchitectureQuantum Mechanics and Applications

A fibre bundle over manifolds of quantum channels and its application to quantum statistics

Fujiwara, Akio, Imai, Hiroshi·2008·Journal of Physics A: Mathematical and Theoretical
DOI 10.1088/1751-8113/41/25/255304
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Abstract

A fibre bundle structure is introduced over manifolds of quantum channels. This structure has a close connection with the problem of estimating an unknown quantum channel Γ θ specified by a parameter θ. It is shown that the quantum Fisher information of the family of output states maximized over all input states , which quantifies the ultimate statistical distinguishability of the parameter θ, is expressed in terms of a geometrical quantity on the fibre bundle. Using this formula, a criterion for the maximum quantum Fisher information of the n th extended channel (id ⊗ Γ θ ) ⊗ n to be O ( n ) is derived. This criterion further proves that for almost all quantum channels, the maximum quantum Fisher information increases in the order of O ( n ).

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Crossref · 10.1088/1751-8113/41/25/255304

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  • The channel-extension bound in equation (16) is an upper bound on the quantum Fisher information that goes around the input state optimization.

    “This leads to an upper bound on , which goes around the input state optimization, yielding42: 16”

    From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [42]

  • Channels that are φ-non-extremal obey standard precision scaling and include all full-rank channels.

    “Channels that have this additional property will be called 'ϕ-non-extremal'. They obey the standard precision scaling, and include all full-rank channels (that is, channels lying in the interior of the SQC)4142.”

    From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [42]

  • A sufficient condition for standard scaling is to find h for which equation (18) holds.

    “the bound equation (16) implies that a sufficient condition for SS is to find h for which , or equivalently42: 18”

    From The elusive Heisenberg limit in quantum-enhanced metrology (2012) · cites this paper as [42]

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Related

Authors
Fujiwara, A., & Imai, H.
Affiliations
The University of Osaka (JP)
ORCID
Fujiwara, Akio
Venue
Journal of Physics A: Mathematical and Theoretical
Publisher
IOP Publishing
Published
2008-05-23
Volume
41
Issue
25
Pages
255304
ISSN
  • 1751-8113 (ISSN-L)
  • 1751-8121
DOI
10.1088/1751-8113/41/25/255304
OpenAlex
W2096109311
Semantic Scholar
544c1275f4bb385ad54aaf1d8b20784c43c1c68e
Cited by
163
References
32
Citations by year
2026: 13 · 2025: 12 · 2024: 13 · 2023: 10 · 2022: 7 · 2021: 19 · 2020: 21 · 2019: 14 · 2018: 6 · 2017: 11 · 2016: 9 · 2015: 8 · 2014: 5 · 2013: 7 · 2012: 4
FWCI
2.11
Type
journal article
Language
en
Open access
closed
Locations
Journal of Physics A Mathematical and Theoretical (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
quantum channels, fiber bundles, quantum Fisher information, quantum parameter estimation, quantum statistics, quantum information geometry

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