Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Efficient tools for quantum metrology with decoherence

Jan Kołodyński, Rafał Demkowicz-Dobrzański

Published Jan 1, 2013• 0 citations
Publisher

Abstract

We propose methods of quantifying precision gain in quantum metrological schemes that correctly incorporate decoherence effects [1], predicting the enhancement to scale super-classically only for moderate-sized probes and limiting the maximal gain to a constant factor.
DOI
10.1364/qim.2013.w6.08

Related papers

General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology

Bruno M. Escher, R. L. de Matos Filho, L. Davidovich

arXiv:1201.1693•Nature Physics•Mar 27, 2011•929 citations

The elusive Heisenberg limit in quantum-enhanced metrology

Rafał Demkowicz-Dobrzański, Jan Kołodyński, Mădălin Guţǎ

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. Quantum metrology employs the properties of quantum states to further enhance the accuracy of some of the most precise measurement schemes to date. Here, a method for estimating the upper bounds to achievable precision in quantum-enhanced metrology protocols in the presence of decoherence is presented.

arXiv:1201.3940•Nature Communications•Sep 18, 2012•773 citations

Heisenberg scaling of time-limited quantum metrology with realistic decoherence

Maxime Hardy, W. A. Coish

Bulletin of the American Physical Society•Feb 28, 2012•0 citations

Efficient tools for quantum metrology with uncorrelated noise

Jan Kołodyński, Rafał Demkowicz-Dobrzański

Quantum metrology offers enhanced performance in experiments on topics such as gravitational wave-detection, magnetometry or atomic clock frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features, such as entanglement or squeezing. For any practical application, the inevitable impact of decoherence needs to be taken into account in order to correctly quantify the ultimate attainable gain in precision. We compare the applicability and the effectiveness of various methods of calculating the ultimate precision bounds resulting from the presence of decoherence. This allows us to place a number of seemingly unrelated concepts into a common framework and arrive at an explicit hierarchy of quantum metrological methods in terms of the tightness of the bounds they provide. In particular, we show a way to extend the techniques originally proposed in Demkowicz-Dobrzański et al (2012 Nature Commun. 3 1063), so that they can be efficiently applied not only in the asymptotic but also in the finite number of particles regime. As a result, we obtain a simple and direct method, yielding bounds that interpolate between the quantum enhanced scaling characteristic for a small number of particles and the asymptotic regime, where quantum enhancement amounts to a constant factor improvement. Methods are applied to numerous models, including noisy phase and frequency estimation, as well as the estimation of the decoherence strength itself.

arXiv:1303.7271•New Journal of Physics•Jul 23, 2013•169 citations

Single-mode quantum metrology enhanced by approximate quantum error correction

Weiting Wang, Zijie Chen, Xinyu Liu +8 more

Bulletin of the American Physical Society•Mar 16, 2021•0 citations

Non-commutativity as a Universal Characterization for Enhanced Quantum Metrology

Ningxin Kong, Haojie Wang, Mingsheng Tian +4 more

A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite $\mathcal{K}$ yields an enhanced scaling of root-mean-square error as $N^{-(1+\mathcal{K})}$. Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit $\mathcal{K} \to \infty$, exponential precision scaling $N^{-1}e^{-N}$ is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.

quant-pharXiv:2511.22280•Physical Review Letters•Nov 28, 2025•3 citations
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. Quantum metrology employs the properties of quantum states to further enhance the accuracy of some of the most precise measurement schemes to date. Here, a method for estimating the upper bounds to achievable precision in quantum-enhanced metrology protocols in the presence of decoherence is presented.
Quantum metrology offers enhanced performance in experiments on topics such as gravitational wave-detection, magnetometry or atomic clock frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features, such as entanglement or squeezing. For any practical application, the inevitable impact of decoherence needs to be taken into account in order to correctly quantify the ultimate attainable gain in precision. We compare the applicability and the effectiveness of various methods of calculating the ultimate precision bounds resulting from the presence of decoherence. This allows us to place a number of seemingly unrelated concepts into a common framework and arrive at an explicit hierarchy of quantum metrological methods in terms of the tightness of the bounds they provide. In particular, we show a way to extend the techniques originally proposed in Demkowicz-Dobrzański et al (2012 Nature Commun. 3 1063), so that they can be efficiently applied not only in the asymptotic but also in the finite number of particles regime. As a result, we obtain a simple and direct method, yielding bounds that interpolate between the quantum enhanced scaling characteristic for a small number of particles and the asymptotic regime, where quantum enhancement amounts to a constant factor improvement. Methods are applied to numerous models, including noisy phase and frequency estimation, as well as the estimation of the decoherence strength itself.
A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index K\mathcal{K}K, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite K\mathcal{K}K yields an enhanced scaling of root-mean-square error as N−(1+K)N^{-(1+\mathcal{K})}N−(1+K). Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit K→∞\mathcal{K} \to \inftyK→∞, exponential precision scaling N−1e−NN^{-1}e^{-N}N−1e−N is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.