Quantum metrology
Open accessAbstract
We point out a general framework that encompasses most cases in which quantum effects enable an increase in precision when estimating a parameter (quantum metrology). The typical quantum precision enhancement is of the order of the square root of the number of times the system is sampled. We prove that this is optimal, and we point out the different strategies (classical and quantum) that permit one to attain this bound.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For an unbiased measurement strategy, the variance of the estimate of an unknown parameter is bounded below by the inverse of the number of repetitions times the quantum Fisher information.
“Under the assumption that our strategy is unbiased, i.e. μ = µ, the uncertainty in our estimate, is related to the variance of μ and is lower bounded by the so-called quantum Cramer-Rao bound”
From Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control (2017) · cites this paper as [99]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Statistical distance and the geometry of quantum states
Braunstein, S. L., & Caves, C. M. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3439 · Cited by 3,176 · see citing works
Quantum-Enhanced Measurements: Beating the Standard Quantum Limit
Giovannetti, V., Lloyd, S., & Maccone, L. (2004) · Science · doi:10.1126/science.1104149 · Cited by 3,014 · see citing works
Self-citationProbabilistic and Statistical Aspects of Quantum Theory
Holevo, A. (2011) · doi:10.1007/978-88-7642-378-9 · Cited by 2,582 · see citing works
SU(2) and SU(1,1) interferometers
Yurke, B., McCall, S. L., & Klauder, J. R. (1986) · Physical Review A · doi:10.1103/physreva.33.4033 · Cited by 1,367 · see citing works
Cleve, R., EKERT, A. K., Macchiavello, C., & Mosca, M. (1998) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.1998.0164 · Cited by 1,279 · see citing works
Optimal frequency measurements with maximally correlated states
Bollinger, J. J., Itano, W. M., Wineland, D. J., & Heinzen, D. J. (1996) · Physical Review A · doi:10.1103/physreva.54.r4649 · Cited by 1,167 · see citing works
Improvement of Frequency Standards with Quantum Entanglement
Huelga, S. F., Macchiavello, C., Pellizzari, T., Ekert, A. K., Plenio, M. B., & Cirac, J. I. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.3865 · Cited by 999 · see citing works
Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors
Abrams, D. S., & Lloyd, S. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.5162 · Cited by 817 · see citing works
Self-citationGeneralized uncertainty relations: Theory, examples, and Lorentz invariance
Braunstein, S. L., Caves, C. M., & Milburn, G. J. (1996) · Annals of Physics · doi:10.1006/aphy.1996.0040 · Cited by 732 · see citing works
Quantum-enhanced positioning and clock synchronization
Giovannetti, V., Lloyd, S., & Maccone, L. (2001) · Nature · doi:10.1038/35086525 · Cited by 500 · see citing works
Self-citationTime in the Quantum Theory and the Uncertainty Relation for Time and Energy
Aharonov, Y., & Bohm, D. (1961) · Physical Review · doi:10.1103/physrev.122.1649 · Cited by 482 · see citing works
Bennett, C. H., & Shor, P. W. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.720553 · Cited by 365 · see citing works
D’Ariano, G. M., & Presti, P. L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.4195 · Cited by 305 · see citing works
Fundamental quantum limit in precision phase measurement
Ou, Z. Y. (1997) · Physical Review A · doi:10.1103/physreva.55.2598 · Cited by 189 · see citing works
Efficient Use of Quantum Resources for the Transmission of a Reference Frame
Chiribella, G., D’Ariano, G. M., Perinotti, P., & Sacchi, M. F. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.180503 · Cited by 126 · see citing works
Quantum methods for clock synchronization: Beating the standard quantum limit without entanglement
de Burgh, M. D., & Bartlett, S. D. (2005) · Physical Review A · doi:10.1103/physreva.72.042301 · Cited by 115 · see citing works
Positioning and clock synchronization through entanglement
Giovannetti, V., Lloyd, S., & Maccone, L. (2002) · Physical Review A · doi:10.1103/physreva.65.022309 · Cited by 113 · see citing works
Self-citationThe role of entanglement in dynamical evolution
Giovannetti, V, Lloyd, S., & Maccone, L. (2003) · Europhysics Letters (EPL) · doi:10.1209/epl/i2003-00418-8 · Cited by 82 · see citing works
Self-citationQuantum Communication Complexity of Establishing a Shared Reference Frame
Rudolph, T., & Grover, L. K. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.217905 · Cited by 67 · see citing works
Measuring energy, estimating Hamiltonians, and the time-energy uncertainty relation
Aharonov, Y., Massar, S., & Popescu, S. (2002) · Physical Review A · doi:10.1103/physreva.66.052107 · Cited by 55 · see citing works
Phase-shift amplification for precision measurements without nonclassical states
Luis, A. (2002) · Physical Review A · doi:10.1103/physreva.65.025802 · Cited by 34 · see citing works
Improving quantum interferometry by using entanglement
D’Ariano, G. M., Paris, M. G. A., & Perinotti, P. (2002) · Physical Review A · doi:10.1103/physreva.65.062106 · Cited by 16 · see citing works
Flagged first, then by citations
Research works printed but not linked: 3
- [1]For a recent review, see V. Giovannetti, S. Lloyd, and L. Maccone, Science 306 , 1330 (2004).
- [2]C. H. Bennett and P. W. Shor, IEEE Trans. Inf. Th. 44 , 2724 (1998).
- [9]A. Y. Kitaev, eprint quant-ph/9511026 (1995); R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Proc. R. Soc. London A 454 , 339 (1998); D. S. Abrams, S. Lloyd, Phys. Rev. Lett. 83 , 5162 (1999). · arXiv
Cited by
Sorted by citations
Degen, C. L., Reinhard, F., & Cappellaro, P. (2017) · Reviews of Modern Physics · doi:10.1103/revmodphys.89.035002 · Cited by 4,045 · see citing works
Giovannetti, V., Lloyd, S., & Maccone, L. (2011) · Nature Photonics · doi:10.1038/nphoton.2011.35 · Cited by 3,894 · see citing works
Self-citationO'Brien, J. L., Furusawa, A., & Vučković, J. (2009) · Nature Photonics · doi:10.1038/nphoton.2009.229 · Cited by 2,388 · see citing works
The classical-quantum boundary for correlations: Discord and related measures
Modi, K., Brodutch, A., Cable, H., Paterek, T., & Vedral, V. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1655 · Cited by 1,600 · see citing works
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
Escher, B. M., de Matos Filho, R. L., & Davidovich, L. (2011) · Nature Physics · doi:10.1038/nphys1958 · Cited by 928 · see citing works
Reference frames, superselection rules, and quantum information
Bartlett, S. D., Rudolph, T., & Spekkens, R. W. (2007) · Reviews of Modern Physics · doi:10.1103/revmodphys.79.555 · Cited by 827 · see citing works
The elusive Heisenberg limit in quantum-enhanced metrology
Demkowicz-Dobrzański, R., Kołodyński, J., & Guţă, M. (2012) · Nature Communications · doi:10.1038/ncomms2067 · Cited by 773 · see citing works
Entanglement-free Heisenberg-limited phase estimation
Higgins, B. L., Berry, D. W., Bartlett, S. D., Wiseman, H. M., & Pryde, G. J. (2007) · Nature · doi:10.1038/nature06257 · Cited by 628 · see citing works
Fisher information and multiparticle entanglement
Hyllus, P., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., & Smerzi, A. (2012) · Physical Review A · doi:10.1103/physreva.85.022321 · Cited by 593 · see citing works
Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control
Deffner, S., & Campbell, S. (2017) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/aa86c6 · Cited by 585 · see citing works
Hybrid Quantum-Classical Algorithms and Quantum Error Mitigation
Endo, S., Cai, Z., Benjamin, S. C., & Yuan, X. (2021) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.90.032001 · Cited by 566 · see citing works
Quantum metrology with entangled coherent states
Joo, J., Munro, W. J., & Spiller, T. P. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.083601 · Cited by 526 · see citing works
Optimal Quantum Phase Estimation
Dorner, U., Demkowicz-Dobrzanski, R., Smith, B. J., Lundeen, J. S., Wasilewski, W., Banaszek, K., & Walmsley, I. A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.040403 · Cited by 494 · see citing works
Quantum-enhanced measurements without entanglement
Braun, D., Adesso, G., Benatti, F., Floreanini, R., Marzolino, U., Mitchell, M. W., & Pirandola, S. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.035006 · Cited by 434 · see citing works
Generalized Limits for Single-Parameter Quantum Estimation
Boixo, S., Flammia, S. T., Caves, C. M., & Geremia, J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.090401 · Cited by 403 · see citing works
Polynomial-time quantum algorithm for the simulation of chemical dynamics
Kassal, I., Jordan, S. P., Love, P. J., Mohseni, M., & Aspuru-Guzik, A. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0808245105 · Cited by 385 · see citing works
Quantum enhanced multiple phase estimation
Humphreys, P. C., Barbieri, M., Datta, A., & Walmsley, I. A. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.070403 · Cited by 379 · see citing works
Quantum phase estimation with lossy interferometers
Demkowicz-Dobrzanski, R., Dorner, U., Smith, B. J., Lundeen, J. S., Wasilewski, W., Banaszek, K., & Walmsley, I. A. (2009) · Physical Review A · doi:10.1103/physreva.80.013825 · Cited by 315 · see citing works
Modular entanglement of atomic qubits using photons and phonons
Hucul, D., Inlek, I. V., Vittorini, G., Crocker, C., Debnath, S., Clark, S. M., & Monroe, C. (2015) · Nature Physics · doi:10.1038/nphys3150 · Cited by 311 · see citing works
Compatibility in multiparameter quantum metrology
Ragy, S., Jarzyna, M., & Demkowicz-Dobrzański, R. (2016) · Physical Review A · doi:10.1103/physreva.94.052108 · Cited by 305 · see citing works
Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving
Deffner, S., Jarzynski, C., & del Campo, A. (2014) · Physical Review X · doi:10.1103/physrevx.4.021013 · Cited by 288 · see citing works
Multi-parameter quantum metrology
Szczykulska, M., Baumgratz, T., & Datta, A. (2016) · Advances in Physics: X · doi:10.1080/23746149.2016.1230476 · Cited by 267 · see citing works
Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
Napolitano, M., Koschorreck, M., Dubost, B., Behbood, N., Sewell, R. J., & Mitchell, M. W. (2011) · Nature · doi:10.1038/nature09778 · Cited by 245 · see citing works
Quantum enhanced estimation of a multidimensional field
Baumgratz, T., & Datta, A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.030801 · Cited by 249 · see citing works
Distributed Quantum Metrology with Linear Networks and Separable Inputs
Ge, W., Jacobs, K., Eldredge, Z., Gorshkov, A. V., & Foss-Feig, M. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.043604 · Cited by 220 · see citing works
Dobšíček, M., Johansson, G., Shumeiko, V., & Wendin, G. (2007) · Physical Review A · doi:10.1103/physreva.76.030306 · Cited by 208 · see citing works
Magnetic field sensing beyond the standard quantum limit under the effect of decoherence
Matsuzaki, Y., Benjamin, S. C., & Fitzsimons, J. (2011) · Physical Review A · doi:10.1103/physreva.84.012103 · Cited by 208 · see citing works
Harnessing the Power of the Second Quantum Revolution
Deutsch, I. H. (2020) · PRX Quantum · doi:10.1103/prxquantum.1.020101 · Cited by 207 · see citing works
Optimal measurements for simultaneous quantum estimation of multiple phases
Pezzè, L., Ciampini, M. A., Spagnolo, N., Humphreys, P. C., Datta, A., Walmsley, I. A., Barbieri, M., Sciarrino, F., & Smerzi, A. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.130504 · Cited by 200 · see citing works
Optimal adaptive control for quantum metrology with time-dependent Hamiltonians
Pang, S., & Jordan, A. N. (2017) · Nature Communications · doi:10.1038/ncomms14695 · Cited by 195 · see citing works
Imany, P., Jaramillo-Villegas, J. A., Odele, O. D., Han, K., Leaird, D. E., Lukens, J. M., Lougovski, P., Qi, M., & Weiner, A. M. (2018) · Optics Express · doi:10.1364/oe.26.001825 · Cited by 185 · see citing works
Quantum interferometry with and without an external phase reference
Jarzyna, M., & Demkowicz-Dobrzański, R. (2012) · Physical Review A · doi:10.1103/physreva.85.011801 · Cited by 182 · see citing works
Quantum metrology for a general Hamiltonian parameter
Pang, S., & Brun, T. A. (2014) · Physical Review A · doi:10.1103/physreva.90.022117 · Cited by 175 · see citing works
Geometric derivation of the quantum speed limit
Jones, P. J., & Kok, P. (2010) · Physical Review A · doi:10.1103/physreva.82.022107 · Cited by 172 · see citing works
Akhlaghi, M. K., Schelew, E., & Young, J. F. (2015) · Nature Communications · doi:10.1038/ncomms9233 · Cited by 166 · see citing works
Sensitivity bounds for multiparameter quantum metrology
Gessner, M., Pezzè, L., & Smerzi, A. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.130503 · Cited by 169 · see citing works
Extremal properties of the variance and the quantum Fisher information
Tóth, G., & Petz, D. (2013) · Physical Review A · doi:10.1103/physreva.87.032324 · Cited by 157 · see citing works
Quantum parameter estimation with optimal control
Liu, J., & Yuan, H. (2017) · Physical Review A · doi:10.1103/physreva.96.012117 · Cited by 133 · see citing works
Multiparameter Gaussian quantum metrology
Nichols, R., Liuzzo-Scorpo, P., Knott, P. A., & Adesso, G. (2018) · Physical Review A · doi:10.1103/physreva.98.012114 · Cited by 131 · see citing works
At the limits of criticality-based quantum metrology: apparent super-Heisenberg scaling revisited
Rams, M. M., Sierant, P., Dutta, O., Horodecki, P., & Zakrzewski, J. (2018) · Physical Review X · doi:10.1103/physrevx.8.021022 · Cited by 160 · see citing works
Pinel, O., Fade, J., Braun, D., Jian, P., Treps, N., & Fabre, C. (2012) · Physical Review A · doi:10.1103/physreva.85.010101 · Cited by 116 · see citing works
Sequential feedback scheme outperforms the parallel scheme for Hamiltonian parameter estimation
Yuan, H. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.160801 · Cited by 112 · see citing works
Simple expression for the quantum Fisher information matrix
Šafránek, D. (2018) · Physical Review A · doi:10.1103/physreva.97.042322 · Cited by 109 · see citing works
Quantum-enhanced multiparameter estimation in multiarm interferometers
Ciampini, M. A., Spagnolo, N., Vitelli, C., Pezzè, L., Smerzi, A., & Sciarrino, F. (2016) · Scientific Reports · doi:10.1038/srep28881 · Cited by 104 · see citing works
Estimation of Gaussian quantum states
Šafránek, D. (2019) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8121/aaf068 · Cited by 110 · see citing works
Improved Quantum Magnetometry beyond the Standard Quantum Limit
Brask, J. B., Chaves, R., & Kołodyński, J. (2015) · Physical Review X · doi:10.1103/physrevx.5.031010 · Cited by 99 · see citing works
Quantum metrology with unitary parametrization processes
Liu, J., Jing, X.-X., & Wang, X. (2015) · Scientific Reports · doi:10.1038/srep08565 · Cited by 95 · see citing works
Experimental multiphase estimation on a chip
Polino, E., Riva, M., Valeri, M., Silvestri, R., Corrielli, G., Crespi, A., Spagnolo, N., Osellame, R., & Sciarrino, F. (2019) · Optica · doi:10.1364/optica.6.000288 · Cited by 101 · see citing works
Experimental phase estimation enhanced by machine learning
Lumino, A., Polino, E., Rab, A. S., Milani, G., Spagnolo, N., Wiebe, N., & Sciarrino, F. (2018) · Physical Review Applied · doi:10.1103/physrevapplied.10.044033 · Cited by 97 · see citing works
Quantum-enhanced metrology for multiple phase estimation with noise
Yue, J.-D., Zhang, Y.-R., & Fan, H. (2014) · Scientific Reports · doi:10.1038/srep05933 · Cited by 84 · see citing works
Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks
Liu, J., Xiong, H.-N., Song, F., & Wang, X. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.05.028 · Cited by 76 · see citing works
Minimizing Estimation Runtime on Noisy Quantum Computers
Wang, G., Koh, D. E., Johnson, P. D., & Cao, Y. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010346 · Cited by 77 · see citing works
Experimental Time-Optimal Universal Control of Spin Qubits in Solids
Geng, J., Wu, Y., Wang, X., Xu, K., Shi, F., Xie, Y., Rong, X., & Du, J. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.170501 · Cited by 68 · see citing works
Control-enhanced sequential scheme for general quantum parameter estimation at the Heisenberg limit
Hou, Z., Wang, R.-J., Tang, J.-F., Yuan, H., Xiang, G.-Y., Li, C.-F., & Guo, G.-C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.123.040501 · Cited by 68 · see citing works
Quantum non-Markovianity based on the Fisher-information matrix
Song, H., Luo, S., & Hong, Y. (2015) · Physical Review A · doi:10.1103/physreva.91.042110 · Cited by 65 · see citing works
Quantum multiparameter estimation with generalized balanced multimode noon-like states
Zhang, L., & Chan, K. W. C. (2017) · Physical Review A · doi:10.1103/physreva.95.032321 · Cited by 54 · see citing works
Entanglement and the speed of evolution of multi-partite quantum systems
Zander, C., Plastino, A. R., Plastino, A., & Casas, M. (2007) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/40/11/020 · Cited by 52 · see citing works
Precision bounds for gradient magnetometry with atomic ensembles
Apellaniz, I., Urizar-Lanz, I., Zimborás, Z., Hyllus, P., & Tóth, G. (2018) · Physical Review A · doi:10.1103/physreva.97.053603 · Cited by 45 · see citing works
Multiple phase estimation for arbitrary pure states under white noise
Yao, Y., Ge, L., Xiao, X., Wang, X., & Sun, C. P. (2014) · Physical Review A · doi:10.1103/physreva.90.062113 · Cited by 42 · see citing works
Quantum metrology of spatial deformation using arrays of classical and quantum light emitters
Sidhu, J. S., & Kok, P. (2017) · Physical Review A · doi:10.1103/physreva.95.063829 · Cited by 31 · see citing works
Multiple phase estimation in quantum cloning machines
Yao, Y., Ge, L., Xiao, X., Wang, X.-G., & Sun, C.-P. (2014) · Physical Review A · doi:10.1103/physreva.90.022327 · Cited by 31 · see citing works
Does large quantum Fisher information imply Bell correlations?
Fröwis, F., Fadel, M., Treutlein, P., Gisin, N., & Brunner, N. (2019) · Physical Review A · doi:10.1103/physreva.99.040101 · Cited by 25 · see citing works
Estimation of gradients in quantum metrology
Altenburg, S., Oszmaniec, M., Wölk, S., & Gühne, O. (2017) · Physical Review A · doi:10.1103/physreva.96.042319 · Cited by 23 · see citing works
Berry curvature as a lower bound for multiparameter estimation
Guo, W., Zhong, W., Jing, X.-X., Fu, L.-B., & Wang, X. (2016) · Physical Review A · doi:10.1103/physreva.93.042115 · Cited by 19 · see citing works
Fisher-information susceptibility for multiparameter quantum estimation
Albarelli, F., Gianani, I., Genoni, M. G., & Barbieri, M. (2024) · Physical Review A · doi:10.1103/physreva.110.032436 · Cited by 6 · see citing works
- Authors
- Giovannetti, V., Lloyd, S., & Maccone, L.
- Affiliations
- Scuola Normale Superiore (IT)
- Massachusetts Institute of Technology (US)
- University of Pavia (IT)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2006-01-03
- Volume
- 96
- Issue
- 1
- Pages
- 010401-010401
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W3037089521
- Cited by
- 2,440
- References
- 22
- Citations by year
- 2026: 185 · 2025: 263 · 2024: 225 · 2023: 171 · 2022: 170 · 2021: 186 · 2020: 196 · 2019: 155 · 2018: 140 · 2017: 126 · 2016: 132 · 2015: 81 · 2014: 86 · 2013: 58 · 2012: 74
- FWCI
- 38.80
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Scuola Normale Superiore di Pisa (submittedVersion, other-oa)
- arXiv (Cornell University)
- 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 metrology, quantum parameter estimation, quantum Fisher information
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
