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arxiv: 2606.07747 · v2 · pith:SMYDK5JAnew · submitted 2026-06-05 · 🪐 quant-ph

100pmDelta t Years of Quantum Uncertainty: From Origins to Modern Insights

Lorcan O. Conlon , Biveen Shajilal , Jie Zhao , Tim C. Ralph , Gerd Leuchs , Ulrik L. Andersen , Syed M. Assad , Ping Koy Lam
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Yunlong Xiao
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Pith reviewed 2026-06-27 21:38 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Heisenberg uncertainty principleuncertainty relationsquantum metrologysqueezed statesmultiparameter estimationquantum mechanics
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The pith

Heisenberg's uncertainty principle has evolved into a spectrum of uncertainty relations that guide precision in quantum metrology.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review traces Heisenberg's 1927 thought experiment on position-momentum disturbance into today's range of mathematical uncertainty relations. It maps the interconnections among those formulations and shows how they underpin strategies for high-precision extraction of information from quantum systems. The paper connects the relations to multiparameter estimation and squeezed states as practical tools in quantum metrology. A sympathetic reader cares because the original principle has moved from foundational theory to limits and protocols that shape real measurements. The review marks the centenary by summarizing a century of development and noting the path ahead.

Core claim

The uncertainty principle began as a thought experiment showing that measuring an electron's position inevitably disturbs its momentum. It has developed into a spectrum of mathematical formulations known as uncertainty relations. These relations are interconnected and play a central role in quantum metrology by underpinning strategies for precision measurements, with explicit links to multiparameter estimation and squeezed states.

What carries the argument

The spectrum of mathematical formulations known as uncertainty relations, which extend the original principle and enable applications in metrology.

Load-bearing premise

The review assumes that the historical narrative, interconnections between formulations, and claimed applications in metrology accurately reflect the cited prior literature without introducing interpretive errors.

What would settle it

A calculation or experiment showing that one of the claimed interconnections between a specific uncertainty relation and a multiparameter estimation bound does not hold as presented would challenge the review's synthesis.

Figures

Figures reproduced from arXiv: 2606.07747 by Biveen Shajilal, Gerd Leuchs, Jie Zhao, Lorcan O. Conlon, Ping Koy Lam, Syed M. Assad, Tim C. Ralph, Ulrik L. Andersen, Yunlong Xiao.

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read the original abstract

Heisenberg's uncertainty principle is a cornerstone of quantum mechanics, marking a decisive departure from classical physics. Conceived almost a century ago through a thought experiment showing that measuring an electron's position inevitably disturbs its momentum, it began as a deceptively simple idea that sparked countless studies and grew into the rich research field it is today. This review traces its development into a spectrum of mathematical formulations -- known as uncertainty relations -- and explores their interconnections and wide-ranging applications. We highlight its central role in quantum metrology, where it underpins strategies for extracting information from quantum systems with ever-increasing precision, and its links to multiparameter estimation and squeezed states. This review, dedicated to the centenary of the uncertainty principle, reflects on how it has deepened our understanding of quantum theory and driven practical advances, and looks ahead to a century poised for further surprising and transformative discoveries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript is a review tracing the historical development of Heisenberg's uncertainty principle from its 1927 origins in a thought experiment to modern mathematical formulations known as uncertainty relations. It examines interconnections among these formulations and their established roles in quantum metrology, multiparameter estimation, and squeezed states, dedicated to the centenary of the principle.

Significance. If the historical narrative and cited interconnections accurately reflect the literature, the review offers a useful synthesis of a foundational topic in quantum mechanics and its applications to precision measurements. The absence of new derivations or quantitative claims means its value lies in overview and context rather than novel results.

minor comments (2)
  1. The abstract refers to a 'spectrum of mathematical formulations' and 'interconnections' without naming specific relations (e.g., Robertson-Schrödinger or entropic forms) or citing key sections; adding an explicit roadmap in §1 would improve clarity for readers.
  2. No equations or tables appear in the provided abstract or overview; if the full text contains them, ensure consistent notation for uncertainty relations across sections to avoid ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of the manuscript and the recommendation to accept. The referee's summary correctly reflects the historical and conceptual scope of the review.

Circularity Check

0 steps flagged

No circularity: historical review with no derivations

full rationale

The paper is a review synthesizing the historical development of Heisenberg's uncertainty principle into modern uncertainty relations and their roles in quantum metrology. It presents no novel derivations, equations, quantitative predictions, or fitted parameters. All content is conceptual and historical overview relying on external cited literature, with no self-referential reductions or load-bearing steps that equate outputs to inputs by construction. This matches the default expectation of no significant circularity for non-derivational papers.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper there are no new free parameters, axioms, or invented entities; all content draws from standard quantum mechanics concepts already present in the cited prior literature.

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Works this paper leans on

300 extracted references · 1 canonical work pages

  1. [1]

    A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Thermodynamic uncertainty relations from ex- change fluctuation theorems, Physical Review Letters 123, 090604 (2019)

    2019

  2. [2]

    Hasegawa and T

    Y. Hasegawa and T. Van Vu, Fluctuation theorem un- certainty relation, Physical Review Letters123, 110602 (2019)

    2019

  3. [3]

    Brandner and K

    K. Brandner and K. Saito, Thermodynamic uncertainty relations for coherent transport, Physical Review Let- ters135, 046302 (2025)

    2025

  4. [4]

    Hasegawa and T

    Y. Hasegawa and T. Nishiyama, Thermodynamic en- tropic uncertainty relation (2025)

    2025

  5. [5]

    Peres,Quantum theory: concepts and methods (Springer, 2002)

    A. Peres,Quantum theory: concepts and methods (Springer, 2002)

    2002

  6. [6]

    Shull, Single-slit diffraction of neutrons, Physical Re- view179, 752 (1969)

    C. Shull, Single-slit diffraction of neutrons, Physical Re- view179, 752 (1969)

    1969

  7. [7]

    Kaiser, S

    H. Kaiser, S. Werner, and E. George, Direct measure- ment of the longitudinal coherence length of a thermal neutron beam, Physical Review Letters50, 560 (1983)

    1983

  8. [8]

    Klein, G

    A. Klein, G. I. Opat, and W. Hamilton, Longitudinal coherence in neutron interferometry, Physical Review Letters50, 563 (1983)

    1983

  9. [9]

    Nairz, M

    O. Nairz, M. Arndt, and A. Zeilinger, Experimen- tal verification of the Heisenberg uncertainty principle for fullerene molecules, Physical Review A65, 032109 (2002)

    2002

  10. [10]

    C. W. Clark, R. Barankov, M. G. Huber, M. Arif, D. G. Cory, and D. A. Pushin, Controlling neutron orbital an- gular momentum, Nature525, 504 (2015)

    2015

  11. [11]

    R. L. Cappelletti, T. Jach, and J. Vinson, Intrinsic or- bital angular momentum states of neutrons, Physical Review Letters120, 090402 (2018)

    2018

  12. [12]

    Shapiro and S

    J. Shapiro and S. Wagner, Phase and amplitude uncer- tainties in heterodyne detection, IEEE Journal of Quan- tum Electronics20, 803 (1984)

    1984

  13. [13]

    Steinlechner, J

    S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schn- abel, Strong Einstein-Podolsky-Rosen steering with un- 67 conditional entangled states, Physical Review A87, 022104 (2013)

    2013

  14. [14]

    Sciarrino, M

    F. Sciarrino, M. Ricci, F. De Martini, R. Filip, and L. Mišta, Realization of a minimal disturbance quan- tum measurement, Physical Review Letters96, 020408 (2006)

    2006

  15. [15]

    U. L. Andersen, M. Sabuncu, R. Filip, and G. Leuchs, Experimental demonstration of coherent state estima- tion with minimal disturbance, Physical Review Letters 96, 020409 (2006)

    2006

  16. [16]

    Banaszek, Fidelity balance in quantum operations, Physical Review Letters86, 1366 (2001)

    K. Banaszek, Fidelity balance in quantum operations, Physical Review Letters86, 1366 (2001)

    2001

  17. [17]

    M. F. Sacchi, Information-disturbance tradeoff in esti- mating a maximally entangled state, Physical Review Letters96, 220502 (2006)

    2006

  18. [18]

    Mišta, Minimal disturbance measurement for co- herent states is non-Gaussian, Physical Review A73, 032335 (2006)

    L. Mišta, Minimal disturbance measurement for co- herent states is non-Gaussian, Physical Review A73, 032335 (2006)

    2006

  19. [19]

    M. G. Genoni and M. G. A. Paris, Information– disturbance tradeoff in continuous-variable Gaussian systems, Physical Review A74, 012301 (2006)

    2006

  20. [20]

    Cavendish, Experiments to determine the density of the earth, Philosophical Transactions of the Royal So- ciety of London , 469 (1798)

    H. Cavendish, Experiments to determine the density of the earth, Philosophical Transactions of the Royal So- ciety of London , 469 (1798)

  21. [21]

    A. A. Michelson and E. W. Morley, On the relative mo- tion of the Earth and the luminiferous ether, American Journal of Science3, 333 (1887)

  22. [22]

    G. Aad, T. Abajyan, B. Abbott, J. Abdallah, S. A. Khalek, A. A. Abdelalim, R. Aben, B. Abi, M. Abolins, O. AbouZeid,et al., Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Physics Letters B716, 1 (2012)

    2012

  23. [23]

    B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Aber- nathy, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R. X. Adhikari,et al., Observation of gravi- tational waves from a binary black hole merger, Physical Review Letters116, 061102 (2016)

    2016

  24. [24]

    C. R. Rao, Information and the accuracy attainable in the estimation of statistical parameters, inBreak- throughs in Statistics(Springer, 1992) pp. 235–247

    1992

  25. [25]

    C. R. Rao, Minimum variance and the estimation of sev- eral parameters, Mathematical Proceedings of the Cam- bridge Philosophical Society43, 280 (1947)

    1947

  26. [26]

    C. W. Helstrom, Minimum mean-squared error of esti- mates in quantum statistics, Physics Letters A25, 101 (1967)

    1967

  27. [27]

    Fujiwara and H

    A. Fujiwara and H. Imai, A fibre bundle over mani- folds of quantum channels and its application to quan- tum statistics, Journal of Physics A: Mathematical and Theoretical41, 255304 (2008)

    2008

  28. [28]

    A. Das, S. K. Yung, L. O. Conlon, Ö. Erkılıç, A. Walsh, Y.-S. Kim, P. K. Lam, S. M. Assad, and J. Zhao, Preci- sion bounds for characterising quantum measurements, Nature Communications (2026)

    2026

  29. [29]

    H. Lee, P. Kok, and J. P. Dowling, A quantum Rosetta stone for interferometry, Journal of Modern Optics49, 2325 (2002)

    2002

  30. [30]

    P. A. M. Dirac, The quantum theory of the emission and absorption of radiation, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character114, 243 (1927)

    1927

  31. [31]

    Conlon,Quantum Multiparameter Estimation: Ex- ploring Fundamental Limits and Testing Quantum Me- chanics, Ph.D

    L. Conlon,Quantum Multiparameter Estimation: Ex- ploring Fundamental Limits and Testing Quantum Me- chanics, Ph.D. thesis, The Australian National Univer- sity (2023)

    2023

  32. [32]

    Jarzyna and R

    M. Jarzyna and R. Demkowicz-Dobrzański, Quantum interferometry with and without an external phase ref- erence, Physical Review A85, 011801 (2012)

    2012

  33. [33]

    Yurke, S

    B. Yurke, S. L. McCall, and J. R. Klauder, SU (2) and SU (1, 1) interferometers, Physical Review A33, 4033 (1986)

    1986

  34. [34]

    J. P. Dowling, Correlated input-port, matter-wave in- terferometer: Quantum-noise limits to the atom-laser gyroscope, Physical Review A57, 4736 (1998)

    1998

  35. [35]

    Yurke, Input states for enhancement of fermion inter- ferometer sensitivity, Physical Review Letters56, 1515 (1986)

    B. Yurke, Input states for enhancement of fermion inter- ferometer sensitivity, Physical Review Letters56, 1515 (1986)

    1986

  36. [36]

    M. G. Genoni, S. Olivares, D. Brivio, S. Cialdi, D. Cipri- ani, A. Santamato, S. Vezzoli, and M. G. Paris, Optical interferometry in the presence of large phase diffusion, Physical Review A85, 043817 (2012)

    2012

  37. [37]

    Tsang, Ziv-Zakai error bounds for quantum param- eter estimation, Physical Review Letters108, 230401 (2012)

    M. Tsang, Ziv-Zakai error bounds for quantum param- eter estimation, Physical Review Letters108, 230401 (2012)

    2012

  38. [38]

    M. J. Holland and K. Burnett, Interferometric detection of optical phase shifts at the Heisenberg limit, Physical Review Letters71, 1355 (1993)

    1993

  39. [39]

    A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Quantum interfero- metric optical lithography: exploiting entanglement to beat the diffraction limit, Physical Review Letters85, 2733 (2000)

    2000

  40. [40]

    Sanders and G

    B. Sanders and G. Milburn, Optimal quantum measure- ments for phase estimation, Physical Review Letters75, 2944 (1995)

    1995

  41. [41]

    Ou, Complementarity and fundamental limit in pre- cision phase measurement, Physical Review Letters77, 2352 (1996)

    Z. Ou, Complementarity and fundamental limit in pre- cision phase measurement, Physical Review Letters77, 2352 (1996)

    1996

  42. [42]

    D. W. Berry, B. L. Higgins, S. D. Bartlett, M. W. Mitchell, G. J. Pryde, and H. M. Wiseman, How to per- form the most accurate possible phase measurements, Physical Review A80, 052114 (2009)

    2009

  43. [43]

    M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, Super-resolving phase measurements with a multipho- ton entangled state, Nature429, 161 (2004)

    2004

  44. [44]

    Walther, J.-W

    P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S.Gasparoni,andA.Zeilinger,DeBrogliewavelengthof a non-local four-photon state, Nature429, 158 (2004)

    2004

  45. [45]

    Nagata, R

    T. Nagata, R. Okamoto, J. L. O’brien, K. Sasaki, and S. Takeuchi, Beating the standard quantum limit with four-entangled photons, Science316, 726 (2007)

    2007

  46. [46]

    Daryanoosh, S

    S. Daryanoosh, S. Slussarenko, D. W. Berry, H. M. Wiseman, and G. J. Pryde, Experimental optical phase measurement approaching the exact Heisenberg limit, Nature Communications9, 4606 (2018)

    2018

  47. [47]

    Slussarenko, M

    S. Slussarenko, M. M. Weston, H. M. Chrzanowski, L. K. Shalm, V. B. Verma, S. W. Nam, and G. J. Pryde, Unconditional violation of the shot-noise limit in photonic quantum metrology, Nature Photonics11, 700 (2017)

    2017

  48. [48]

    Gao, C.-Y

    W.-B. Gao, C.-Y. Lu, X.-C. Yao, P. Xu, O. Gühne, A. Goebel, Y.-A. Chen, C.-Z. Peng, Z.-B. Chen, and J.-W. Pan, Experimental demonstration of a hyper- entangled ten-qubit Schrödinger cat state, Nature Physics6, 331 (2010)

    2010

  49. [49]

    Wang, L.-K

    X.-L. Wang, L.-K. Chen, W. Li, H.-L. Huang, C. Liu, C. Chen, Y.-H. Luo, Z.-E. Su, D. Wu, Z.-D. Li,et al., 68 Experimental ten-photon entanglement, Physical Re- view Letters117, 210502 (2016)

    2016

  50. [50]

    C. You, M. Hong, P. Bierhorst, A. E. Lita, S. Glancy, S. Kolthammer, E. Knill, S. W. Nam, R. P. Mirin, O. S. Magaña-Loaiza, and T. Gerrits, Scalable multi- photon quantum metrology with neither pre- nor post- selected measurements, Applied Physics Reviews8, 041406 (2021)

    2021

  51. [51]

    Pezzé and A

    L. Pezzé and A. Smerzi, Mach-Zehnder interferometry at the Heisenberg limit with coherent and squeezed- vacuum light, Physical Review Letters100, 073601 (2008)

    2008

  52. [52]

    M. e. Tse, H. Yu, N. Kijbunchoo, A. Fernandez-Galiana, P. Dupej, L. Barsotti, C. Blair, D. Brown, S. Dwyer, A. Effler,et al., Quantum-enhanced advanced LIGO de- tectorsintheeraofgravitational-waveastronomy,Phys- ical Review Letters123, 231107 (2019)

    2019

  53. [53]

    M. D. Lang and C. M. Caves, Optimal quantum- enhanced interferometry using a laser power source, Physical Review Letters111, 173601 (2013)

    2013

  54. [54]

    Monras, Optimal phase measurements with pure Gaussian states, Physical Review A73, 033821 (2006)

    A. Monras, Optimal phase measurements with pure Gaussian states, Physical Review A73, 033821 (2006)

    2006

  55. [55]

    P. M. Anisimov, G. M. Raterman, A. Chiruvelli, W. N. Plick, S. D. Huver, H. Lee, and J. P. Dowling, Quan- tum metrology with two-mode squeezed vacuum: parity detection beats the Heisenberg limit, Physical Review Letters104, 103602 (2010)

    2010

  56. [56]

    Olivares and M

    S. Olivares and M. Paris, Optimized interferometry with Gaussian states, Optics and Spectroscopy103, 231 (2007)

    2007

  57. [57]

    J. A. Nielsen, J. S. Neergaard-Nielsen, T. Gehring, and U. L. Andersen, Deterministic quantum phase estima- tion beyond N00N states, Physical Review Letters130, 123603 (2023)

    2023

  58. [58]

    B. Li, A. Das, S. Tserkis, P. Narang, P. K. Lam, and S. M. Assad, On the equivalence between squeezing and entanglement potential for two-mode Gaussian states, Scientific Reports13, 11722 (2023)

    2023

  59. [59]

    Huntington, G

    E. Huntington, G. Milford, C. Robilliard, T. Ralph, O. Glöckl, U. L. Andersen, S. Lorenz, and G. Leuchs, Demonstrationofthespatialseparationoftheentangled quantum sidebands of an optical field, Physical Review A—Atomic, Molecular, and Optical Physics71, 041802 (2005)

    2005

  60. [60]

    Sahota and N

    J. Sahota and N. Quesada, Quantum correlations in op- tical metrology: Heisenberg-limited phase estimation without mode entanglement, Physical Review A91, 013808 (2015)

    2015

  61. [61]

    D. M. Greenberger, M. A. Horne, and A. Zeilinger, Go- ing beyond Bell’s theorem, inBell’s theorem, quantum theory and conceptions of the universe(Springer, 1989) pp. 69–72

    1989

  62. [62]

    Huang, M

    J. Huang, M. Zhuang, and C. Lee, Entanglement- enhanced quantum metrology: From standard quantum limit to heisenberg limit, Applied Physics Reviews11, 031302 (2024)

    2024

  63. [63]

    Braun, G

    D. Braun, G. Adesso, F. Benatti, R. Floreanini, U. Mar- zolino, M. W. Mitchell, and S. Pirandola, Quantum- enhanced measurements without entanglement, Re- views of Modern Physics90, 035006 (2018)

    2018

  64. [64]

    L. J. Fiderer and D. Braun, Quantum metrology with quantum-chaotic sensors, Nature Communications9, 1351 (2018)

    2018

  65. [65]

    B. L. Higgins, D. W. Berry, S. D. Bartlett, H. M. Wise- man, and G. J. Pryde, Entanglement-free Heisenberg- limited phase estimation, Nature450, 393 (2007)

    2007

  66. [66]

    C. A. Casacio, L. S. Madsen, A. Terrasson, M. Waleed, K. Barnscheidt, B. Hage, M. A. Taylor, and W. P. Bowen, Quantum-enhanced nonlinear microscopy, Na- ture594, 201 (2021)

    2021

  67. [67]

    A. Cao, W. J. Eckner, T. Lukin Yelin, A. W. Young, S. Jandura, L. Yan, K. Kim, G. Pupillo, J. Ye, N. Dark- wah Oppong,et al., Multi-qubit gates and Schrödinger cat states in an optical clock, Nature634, 315 (2024)

    2024

  68. [68]

    Finkelstein, R

    R. Finkelstein, R. B.-S. Tsai, X. Sun, P. Scholl, S. Di- rekci, T. Gefen, J. Choi, A. L. Shaw, and M. Endres, Universal quantum operations and ancilla-based read- out for tweezer clocks, Nature634, 321 (2024)

    2024

  69. [69]

    Kacprowicz, R

    M. Kacprowicz, R. Demkowicz-Dobrzański, W. Wasilewski, K. Banaszek, and I. Walmsley, Experimental quantum-enhanced estimation of a lossy phase shift, Nature Photonics4, 357 (2010)

    2010

  70. [70]

    X. Guo, C. R. Breum, J. Borregaard, S. Izumi, M. V. Larsen, T. Gehring, M. Christandl, J. S. Neergaard- Nielsen, and U. L. Andersen, Distributed quantum sens- ing in a continuous-variable entangled network, Nature Physics16, 281 (2020)

    2020

  71. [71]

    K. C. McCormick, J. Keller, S. C. Burd, D. J. Wineland, A. C. Wilson, and D. Leibfried, Quantum-enhanced sensing of a single-ion mechanical oscillator, Nature 572, 86 (2019)

    2019

  72. [72]

    Leibfried, M

    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 spec- troscopy with multiparticle entangled states, Science 304, 1476 (2004)

    2004

  73. [73]

    W. Wang, Y. Wu, Y. Ma, W. Cai, L. Hu, X. Mu, Y. Xu, Z.-J. Chen, H. Wang, Y. Song,et al., Heisenberg-limited single-mode quantum metrology in a superconducting circuit, Nature Communications10, 1 (2019)

    2019

  74. [74]

    Muessel, H

    W. Muessel, H. Strobel, D. Linnemann, D. Hume, and M. Oberthaler, Scalable spin squeezing for quantum- enhanced magnetometry with Bose-Einstein conden- sates, Physical Review Letters113, 103004 (2014)

    2014

  75. [75]

    Gross, T

    C. Gross, T. Zibold, E. Nicklas, J. Esteve, and M. K. Oberthaler, Nonlinear atom interferometer surpasses classical precision limit, Nature464, 1165 (2010)

    2010

  76. [76]

    Demkowicz-Dobrzański, M

    R. Demkowicz-Dobrzański, M. Jarzyna, and J. Kołodyński, Quantum limits in optical interfer- ometry, Progress in Optics60, 345 (2015)

    2015

  77. [77]

    Datta, Sensing with quantum light: a perspective, Nanophotonics 10.1515/nanoph-2024-0649 (2025)

    A. Datta, Sensing with quantum light: a perspective, Nanophotonics 10.1515/nanoph-2024-0649 (2025)

    work page doi:10.1515/nanoph-2024-0649 2024

  78. [78]

    K. T. Kapale, L. D. Didomenico, H. Lee, P. Kok, and J. P. Dowling, Quantum interferometric sensors, in Noise and Fluctuations in Photonics, Quantum Optics, and Communications, Vol. 6603 (SPIE, 2007) pp. 301– 308

    2007

  79. [79]

    J. P. Dowling, Quantum optical metrology–the lowdown on high-N00N states, Contemporary physics49, 125 (2008)

    2008

  80. [80]

    Barbieri, Optical quantum metrology, PRX Quan- tum3, 010202 (2022)

    M. Barbieri, Optical quantum metrology, PRX Quan- tum3, 010202 (2022)

    2022

Showing first 80 references.