Metrologically optimal quantum states under noise
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AbstractWe propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologically optimal and efficient measurement protocol utilizing time-reversed dynamics and single-qubit on-site measurements. Using quantum domino dynamics, we also present a protocol free of the time-reversal step that has an estimation error roughly twice the best possible value. Finally, we show that spin squeezed states are also optimal for noisy metrology under general conditions.► BibTeX data@article{Yin2026metrologically, doi = {10.22331/q-2026-04-01-2050}, url = {https://doi.org/10.22331/q-2026-04-01-2050}, title = {Metrologically optimal quantum states under noise}, author = {Yin, Chao and Albert, Victor V. and Zhou, Sisi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2050}, month = apr, year = {2026} }► References [1] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. ``Advances in quantum metrology''. Nature photonics 5, 222–229 (2011). https://doi.org/10.1038/nphoton.2011.35 [2] C. L. Degen, F. Reinhard, and P. Cappellaro. ``Quantum sensing''. Rev. Mod. Phys. 89, 035002 (2017). https://doi.org/10.1103/RevModPhys.89.035002 [3] Luca Pezzè, Augusto Smerzi, Markus K. 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Physical Review Research 4, 033092 (2022). https://doi.org/10.1103/PhysRevResearch.4.033092Cited byCould not fetch Crossref cited-by data during last attempt 2026-04-01 11:42:37: Could not fetch cited-by data for 10.22331/q-2026-04-01-2050 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-04-01 11:42:37: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologically optimal and efficient measurement protocol utilizing time-reversed dynamics and single-qubit on-site measurements. Using quantum domino dynamics, we also present a protocol free of the time-reversal step that has an estimation error roughly twice the best possible value. Finally, we show that spin squeezed states are also optimal for noisy metrology under general conditions.► BibTeX data@article{Yin2026metrologically, doi = {10.22331/q-2026-04-01-2050}, url = {https://doi.org/10.22331/q-2026-04-01-2050}, title = {Metrologically optimal quantum states under noise}, author = {Yin, Chao and Albert, Victor V. and Zhou, Sisi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2050}, month = apr, year = {2026} }► References [1] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. ``Advances in quantum metrology''. Nature photonics 5, 222–229 (2011). https://doi.org/10.1038/nphoton.2011.35 [2] C. L. Degen, F. Reinhard, and P. Cappellaro. ``Quantum sensing''. Rev. Mod. Phys. 89, 035002 (2017). https://doi.org/10.1103/RevModPhys.89.035002 [3] Luca Pezzè, Augusto Smerzi, Markus K. Oberthaler, Roman Schmied, and Philipp Treutlein. ``Quantum metrology with nonclassical states of atomic ensembles''. Rev. Mod. Phys. 90, 035005 (2018). https://doi.org/10.1103/RevModPhys.90.035005 [4] Stefano Pirandola, Bhaskar Roy Bardhan, Tobias Gehring, Christian Weedbrook, and Seth Lloyd. ``Advances in photonic quantum sensing''. Nat. Photonics. 12, 724 (2018). https://doi.org/10.1038/s41566-018-0301-6 [5] Carlton M. Caves. ``Quantum-mechanical noise in an interferometer''. Phys. Rev. D 23, 1693–1708 (1981). https://doi.org/10.1103/PhysRevD.23.1693 [6] Bernard Yurke, Samuel L. McCall, and John R. Klauder. ``Su(2) and su(1,1) interferometers''. Phys. Rev. A 33, 4033–4054 (1986). https://doi.org/10.1103/PhysRevA.33.4033 [7] LIGO Collaboration. ``A gravitational wave observatory operating beyond the quantum shot-noise limit''. Nature Physics 7, 962–965 (2011). https://doi.org/10.1038/nphys2083 [8] LIGO Collaboration. ``Enhanced sensitivity of the ligo gravitational wave detector by using squeezed states of light''. Nature Photonics 7, 613–619 (2013). https://doi.org/10.1038/nphoton.2013.177 [9] David Le Sage, Koji Arai, David R Glenn, Stephen J DeVience, Linh M Pham, Lilah Rahn-Lee, Mikhail D Lukin, Amir Yacoby, Arash Komeili, and Ronald L Walsworth. ``Optical magnetic imaging of living cells''. Nature 496, 486–489 (2013). https://doi.org/10.1038/nature12072 [10] Gabriela Barreto Lemos, Victoria Borish, Garrett D Cole, Sven Ramelow, Radek Lapkiewicz, and Anton Zeilinger. ``Quantum imaging with undetected photons''. Nature 512, 409–412 (2014). https://doi.org/10.1038/nature13586 [11] Mankei Tsang, Ranjith Nair, and Xiao-Ming Lu. ``Quantum theory of superresolution for two incoherent optical point sources''. Physical Review X 6, 031033 (2016). https://doi.org/10.1103/PhysRevX.6.031033 [12] MH Abobeih, J Randall, CE Bradley, HP Bartling, MA Bakker, MJ Degen, M Markham, DJ Twitchen, and TH Taminiau. ``Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor''. Nature 576, 411–415 (2019). https://doi.org/10.1038/s41586-019-1834-7 [13] D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen. ``Spin squeezing and reduced quantum noise in spectroscopy''. Phys. Rev. A 46, R6797–R6800 (1992). https://doi.org/10.1103/PhysRevA.46.R6797 [14] J. J. Bollinger, Wayne M. Itano, D. J. Wineland, and D. J. Heinzen. ``Optimal frequency measurements with maximally correlated states''. Phys. Rev. A 54, R4649–R4652 (1996). https://doi.org/10.1103/PhysRevA.54.R4649 [15] D. Leibfried, M. D. Barrett, T. Schaetz, J. Britton, J. Chiaverini, W. M. Itano, J. D. Jost, C. Langer, and D. J. Wineland. ``Toward heisenberg-limited spectroscopy with multiparticle entangled states''. Science 304, 1476–1478 (2004). https://doi.org/10.1126/science.1097576 [16] JM Taylor, Paola Cappellaro, L Childress, Liang Jiang, Dmitry Budker, PR Hemmer, Amir Yacoby, R Walsworth, and MD Lukin. ``High-sensitivity diamond magnetometer with nanoscale resolution''. Nature Physics 4, 810–816 (2008). https://doi.org/10.1038/nphys1075 [17] Hengyun Zhou, Joonhee Choi, Soonwon Choi, Renate Landig, Alexander M Douglas, Junichi Isoya, Fedor Jelezko, Shinobu Onoda, Hitoshi Sumiya, Paola Cappellaro, et al. ``Quantum metrology with strongly interacting spin systems''. Physical review X 10, 031003 (2020). https://doi.org/10.1103/PhysRevX.10.031003 [18] Till Rosenband, DB Hume, PO Schmidt, Chin-Wen Chou, Anders Brusch, Luca Lorini, WH Oskay, Robert E Drullinger, Tara M Fortier, Jason E Stalnaker, et al. ``Frequency ratio of al+ and hg+ single-ion optical clocks; metrology at the 17th decimal place''. Science 319, 1808–1812 (2008). https://doi.org/10.1126/science.1154622 [19] Jürgen Appel, Patrick Joachim Windpassinger, Daniel Oblak, U Busk Hoff, Niels Kjærgaard, and Eugene Simon Polzik. ``Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit''. Proceedings of the National Academy of Sciences 106, 10960–10965 (2009). https://doi.org/10.1073/pnas.0901550106 [20] Andrew D Ludlow, Martin M Boyd, Jun Ye, Ekkehard Peik, and Piet O Schmidt. ``Optical atomic clocks''. Reviews of Modern Physics 87, 637 (2015). https://doi.org/10.1103/RevModPhys.87.637 [21] Raphael Kaubruegger, Denis V Vasilyev, Marius Schulte, Klemens Hammerer, and Peter Zoller. ``Quantum variational optimization of ramsey interferometry and atomic clocks''. 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