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The elusive Heisenberg limit in quantum-enhanced metrology

Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N bein...

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Autores principales: Demkowicz-Dobrzański, Rafał, Kołodyński, Jan, Guţă, Mădălin
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Pub. Group 2012
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658100/
https://www.ncbi.nlm.nih.gov/pubmed/22990859
http://dx.doi.org/10.1038/ncomms2067
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author Demkowicz-Dobrzański, Rafał
Kołodyński, Jan
Guţă, Mădălin
author_facet Demkowicz-Dobrzański, Rafał
Kołodyński, Jan
Guţă, Mădălin
author_sort Demkowicz-Dobrzański, Rafał
collection PubMed
description Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss.
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spelling pubmed-36581002013-05-20 The elusive Heisenberg limit in quantum-enhanced metrology Demkowicz-Dobrzański, Rafał Kołodyński, Jan Guţă, Mădălin Nat Commun Article Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. Nature Pub. Group 2012-09-18 /pmc/articles/PMC3658100/ /pubmed/22990859 http://dx.doi.org/10.1038/ncomms2067 Text en Copyright © 2012, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved. http://creativecommons.org/licenses/by-nc-sa/3.0/ This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/
spellingShingle Article
Demkowicz-Dobrzański, Rafał
Kołodyński, Jan
Guţă, Mădălin
The elusive Heisenberg limit in quantum-enhanced metrology
title The elusive Heisenberg limit in quantum-enhanced metrology
title_full The elusive Heisenberg limit in quantum-enhanced metrology
title_fullStr The elusive Heisenberg limit in quantum-enhanced metrology
title_full_unstemmed The elusive Heisenberg limit in quantum-enhanced metrology
title_short The elusive Heisenberg limit in quantum-enhanced metrology
title_sort elusive heisenberg limit in quantum-enhanced metrology
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3658100/
https://www.ncbi.nlm.nih.gov/pubmed/22990859
http://dx.doi.org/10.1038/ncomms2067
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