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Sequential analysis in a continuous spin-noise quantum sensor

E. Roda-Salichs1,*, G. Gasbarri1,†, A. Alou1,2,‡, M. Skotiniotis1,§, A. Sierant3, D. Méndez-Avalos3, M. W. Mitchell3,4,∥, and J. Calsamiglia1,¶

  • *Contact author: elisabet.roda@uab.cat
  • †Present address: Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany.
  • ‡Present address: Port d’Informació Científica (PIC), Campus UAB, C. Albareda s/n, 08193 Bellaterra, Spain.
  • §Present address: Quantum Thermodynamics and Computation Group, Department of Electromagnetism and Condensed Matter, Universidad de Granada, 18071 Granada, Spain and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain.
  • ∥Contact author: morgan.mitchell@icfo.eu
  • Contact author: john.calsamiglia@uab.cat
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Phys. Rev. Research 8, 033038 – Published 9 July, 2026

DOI: https://doi.org/10.1103/z7zj-864q

Abstract

Many control and detection applications require real-time analysis of signals from sensors, in order to quickly and accurately act upon events revealed by the sensors. Such signal analysis benefits from statistical models of signal and sensor behavior. This creates a need for data analysis methods that are simultaneously model based, computationally efficient, and causal, in the sense that they employ only sensor data available prior to a specific point in time. In this work, we implement sequential data analysis techniques on a spin-noise-based quantum sensor to perform two key tasks: hypothesis testing and quickest change-point detection. These online protocols allow us to detect weak magnetic fields by adaptively collecting measurement data until a predefined confidence threshold is reached. We demonstrate these methods in a realistic experimental setting and derive performance bounds for the achievable precision and response time. Our approach has potential utility when detecting small perturbations to the magnetic field, in both applied and fundamental contexts including biomagnetism, geophysical surveys, detection of concealed materials, searches for dark matter candidates, and exotic spin interactions. Our results demonstrate that sequential techniques enable faster and more sensitive detection, making them a powerful tool for quantum sensing.

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References (85)

  1. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2009).
  2. J. Kitching, S. Knappe, and E. A. Donley, Atomic sensors—A review, IEEE Sens. J. 11, 1749 (2011).
  3. A. Serafini, Feedback control in quantum optics: An overview of experimental breakthroughs and areas of application, Int. Scholarly Res. Not. 2012, 275016 (2012).
  4. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86, 1391 (2014).
  5. B. Rogers, N. Lo Gullo, G. De Chiara, G. M. Palma, and M. Paternostro, Hybrid optomechanics for quantum technologies, Quantum Meas. Quantum Metrol. 2, 000010247820140002 (2014).
  6. W. Yu, W. C. Jiang, Q. Lin, and T. Lu, Cavity optomechanical spring sensing of single molecules, Nat. Commun. 7, 12311 (2016).
  7. J. Millen, T. S. Monteiro, R. Pettit, and A. N. Vamivakas, Optomechanics with levitated particles, Rep. Prog. Phys. 83, 026401 (2020).
  8. P. Kumar, T. Biswas, K. Feliz, R. Kanamoto, M.-S. Chang, A. K. Jha, and M. Bhattacharya, Cavity optomechanical sensing and manipulation of an atomic persistent current, Phys. Rev. Lett. 127, 113601 (2021).
  9. B.-B. Li, L. Ou, Y. Lei, and Y.-C. Liu, Cavity optomechanical sensing, Nanophotonics 10, 2799 (2021).
  10. S. Barzanjeh, A. Xuereb, S. Gröblacher, M. Paternostro, C. A. Regal, and E. M. Weig, Optomechanics for quantum technologies, Nat. Phys. 18, 15 (2022).
  11. S. Z. Ang, G. I. Harris, W. P. Bowen, and M. Tsang, Optomechanical parameter estimation, New J. Phys. 15, 103028 (2013).
  12. D. Budker and M. Romalis, Optical magnetometry, Nat. Phys. 3, 227 (2007).
  13. H. M. Wiseman and G. J. Milburn, Quantum theory of field-quadrature measurements, Phys. Rev. A 47, 642 (1993).
  14. J. Kitching, Chip-scale atomic devices, Appl. Phys. Rev. 5, 031302 (2018).
  15. S. Forstner, J. Knittel, E. Sheridan, J. D. Swaim, H. Rubinsztein-Dunlop, and W. P. Bowen, Sensitivity and performance of cavity optomechanical field sensors, Photon. Sens. 2, 259 (2012).
  16. M. Tsang, Continuous quantum hypothesis testing, Phys. Rev. Lett. 108, 170502 (2012).
  17. K. Jacobs, Quantum Measurement Theory and its Applications (Cambridge University Press, Cambridge, 2014).
  18. K. Mølmer, Hypothesis testing with open quantum systems, Phys. Rev. Lett. 114, 040401 (2015).
  19. F. Albarelli, M. A. C. Rossi, M. G. A. Paris, and M. G. Genoni, Ultimate limits for quantum magnetometry via time-continuous measurements, New J. Phys. 19, 123011 (2017).
  20. A. H. Kiilerich and K. Mølmer, Hypothesis testing with a continuously monitored quantum system, Phys. Rev. A 98, 022103 (2018).
  21. J. F. Ralph, M. Toroš, S. Maskell, K. Jacobs, M. Rashid, A. J. Setter, and H. Ulbricht, Dynamical model selection near the quantum-classical boundary, Phys. Rev. A 98, 010102(R) (2018).
  22. R. Jiménez-Martínez, J. Kołodyński, C. Troullinou, V. G. Lucivero, J. Kong, and M. W. Mitchell, Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering, Phys. Rev. Lett. 120, 040503 (2018).
  23. J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum Fisher information matrix and multiparameter estimation, J. Phys. A: Math. Theor. 53, 023001 (2020).
  24. M. W. Mitchell and S. Palacios Alvarez, Colloquium: Quantum limits to the energy resolution of magnetic field sensors, Rev. Mod. Phys. 92, 021001 (2020).
  25. J. Amorós-Binefa and J. Kołodyński, Noisy atomic magnetometry in real time, New J. Phys. 23, 123030 (2021).
  26. M. M. Marchese, A. Belenchia, and M. Paternostro, Optomechanics-based quantum estimation theory for collapse models, Entropy 25, 500 (2023).
  27. M. Wang, D. J. Perez-Morelo, G. Ramer, G. Pavlidis, J. J. Schwartz, L. Yu, R. Ilic, A. Centrone, and V. A. Aksyuk, Beating thermal noise in a dynamic signal measurement by a nanofabricated cavity optomechanical sensor, Sci. Adv. 9, eadf7595 (2023).
  28. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  29. J. Amorós-Binefa and J. Kołodyński, Noisy atomic magnetometry with Kalman filtering and measurement-based feedback, PRX Quantum 6, 030331 (2025).
  30. A. Wald, Sequential tests of statistical hypotheses, Ann. Math. Stat. 16, 117 (1945).
  31. A. Tartakovsky, I. Nikiforov, and M. Basseville, Sequential Analysis: Hypothesis Testing and Changepoint Detection (CRC Press, New York, 2014).
  32. A. Ramdas, P. Grünwald, V. Vovk, and G. Shafer, Game-theoretic statistics and safe anytime-valid inference, Stat. Sci. 38, 576 (2023).
  33. E. Martínez Vargas, C. Hirche, G. Sentís, M. Skotiniotis, M. Carrizo, R. Muñoz Tapia, and J. Calsamiglia, Quantum sequential hypothesis testing, Phys. Rev. Lett. 126, 180502 (2021).
  34. Y. Li, V. Y. F. Tan, and M. Tomamichel, Optimal adaptive strategies for sequential quantum hypothesis testing, Commun. Math. Phys. 392, 993 (2022).
  35. G. Lorden, Procedures for reacting to a change in distribution, Ann. Math. Stat. 42, 1897 (1971).
  36. M. Fanizza, C. Hirche, and J. Calsamiglia, Ultimate limits for quickest quantum change-point detection, Phys. Rev. Lett. 131, 020602 (2023).
  37. M. Reichert, Q. Zhuang, J. H. Shapiro, and R. Di Candia, Quantum illumination with a hetero-homodyne receiver and sequential detection, Phys. Rev. Appl. 20, 014030 (2023).
  38. Z. Gong and S. Guha, Quantum-enhanced change detection and joint communication-detection, Phys. Rev. A 112, 032604 (2025).
  39. S. Guha, T. C. John, and P. Basu, Quantum-enhanced quickest change detection of transmission loss, Phys. Rev. Lett. 135, 210801 (2025).
  40. C. Ahn, A. C. Doherty, and A. J. Landahl, Continuous quantum error correction via quantum feedback control, Phys. Rev. A 65, 042301 (2002).
  41. W. P. Livingston, M. S. Blok, E. Flurin, J. Dressel, A. N. Jordan, and I. Siddiqi, Experimental demonstration of continuous quantum error correction, Nat. Commun. 13, 2307 (2022).
  42. G. Gasbarri, M. Bilkis, E. Roda-Salichs, and J. Calsamiglia, Sequential hypothesis testing for continuously-monitored quantum systems, Quantum 8, 1289 (2024).
  43. E. Boto, S. S. Meyer, V. Shah, O. Alem, S. Knappe, P. Kruger, T. M. Fromhold, M. Lim, P. M. Glover, P. G. Morris, R. Bowtell, G. R. Barnes, and M. J. Brookes, A new generation of magnetoencephalography: Room temperature measurements using optically-pumped magnetometers, NeuroImage 149, 404 (2017).
  44. E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. S. Meyer, L. D. Muñoz, K. J. Mullinger, T. M. Tierney, S. Bestmann, G. R. Barnes, R. Bowtell, and M. J. Brookes, Moving magnetoencephalography towards real-world applications with a wearable system, Nature (London) 555, 657 (2018).
  45. S. Knappe, Y. Okada, and S. Krzyzewski, U.S. Patent No. 12,019,127 (U.S. Patent and Trademark Office, Washington, DC, 2024).
  46. G. Oelsner, R. IJsselsteijn, T. Scholtes, A. Krüger, V. Schultze, G. Seyffert, G. Werner, M. Jäger, A. Chwala, and R. Stolz, Integrated optically pumped magnetometer for measurements within Earth’s magnetic field, Phys. Rev. Appl. 17, 024034 (2022).
  47. M. S. Mrozowski, A. S. Bell, P. F. Griffin, D. Hunter, D. Burt, J. P. McGilligan, E. Riis, C. D. Beggan, and S. J. Ingleby, Distributed network of optically pumped magnetometers for space weather monitoring, Sci. Rep. 14, 28229 (2024).
  48. L. Hunter, J. Gordon, S. Peck, D. Ang, and J.-F. Lin, Using the earth as a polarized electron source to search for long-range spin-spin interactions, Science 339, 928 (2013).
  49. M. S. Safronova, D. Budker, D. DeMille, D. F. J. Kimball, A. Derevianko, and C. W. Clark, Search for new physics with atoms and molecules, Rev. Mod. Phys. 90, 025008 (2018).
  50. N. A. Sinitsyn and Y. V. Pershin, The theory of spin noise spectroscopy: A review, Rep. Prog. Phys. 79, 106501 (2016).
  51. V. S. Zapasskii, Spin-noise spectroscopy: From proof of principle to applications, Adv. Opt. Photon. 5, 131 (2013).
  52. S. A. Crooker, D. G. Rickel, A. V. Balatsky, and D. L. Smith, Spectroscopy of spontaneous spin noise as a probe of spin dynamics and magnetic resonance, Nature (London) 431, 49 (2004).
  53. V. G. Lucivero, R. Jiménez-Martínez, J. Kong, and M. W. Mitchell, Squeezed-light spin noise spectroscopy, Phys. Rev. A 93, 053802 (2016).
  54. V. G. Lucivero, A. Dimic, J. Kong, R. Jiménez-Martínez, and M. W. Mitchell, Sensitivity, quantum limits, and quantum enhancement of noise spectroscopies, Phys. Rev. A 95, 041803(R) (2017).
  55. J. Kong, R. Jiménez-Martínez, C. Troullinou, V. G. Lucivero, G. Tóth, and M. W. Mitchell, Measurement-induced, spatially-extended entanglement in a hot, strongly-interacting atomic system, Nat. Commun. 11, 2415 (2020).
  56. K. Mouloudakis, F. Vouzinas, A. Margaritakis, A. Koutsimpela, G. Mouloudakis, V. Koutrouli, M. Skotiniotis, G. P. Tsironis, M. Loulakis, M. W. Mitchell, G. Vasilakis, and I. K. Kominis, Interspecies spin-noise correlations in hot atomic vapors, Phys. Rev. A 108, 052822 (2023).
  57. K. Mouloudakis, G. Vasilakis, V. G. Lucivero, J. Kong, I. K. Kominis, and M. W. Mitchell, Effects of spin-exchange collisions on the fluctuation spectra of hot alkali-metal vapors, Phys. Rev. A 106, 023112 (2022).
  58. K. Mouloudakis, J. Kong, A. Sierant, E. Arkin, M. Hernández Ruiz, R. Jiménez-Martínez, and M. W. Mitchell, Anomalous noise spectra in a spin-exchange-relaxation-free alkali-metal vapor, Phys. Rev. A 109, L040802 (2024).
  59. T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley Series in Telecommunications and Signal Processing (Wiley-Interscience, New York, 2006).
  60. D. Kazakos and P. Papantoni-Kazakos, Spectral distance measures between Gaussian processes, IEEE Trans. Autom. Control 25, 950 (1980).
  61. A. Wald, Sequential Analysis (Courier Corporation, New York, 2004).
  62. A. Wald and J. Wolfowitz, Optimum character of the sequential probability ratio test, Ann. Math. Stat. 19, 326 (1948).
  63. E. S. Page, Continuous inspection schemes, Biometrika 41, 100 (1954).
  64. G. V. Moustakides, Optimal stopping times for detecting changes in distributions, Ann. Stat. 14, 1379 (1986).
  65. Y. Ritov, Decision theoretic optimality of the cusum procedure, Ann. Stat. 18, 1464 (1990).
  66. T. L. Lai, Information bounds and quick detection of parameter changes in stochastic systems, IEEE Trans. Inf. Theory 44, 2917 (1998).
  67. J. Kong, V. G. Lucivero, R. Jiménez-Martínez, and M. W. Mitchell, Long-term laser frequency stabilization using fiber interferometers, Rev. Sci. Instrum. 86, 073104 (2015).
  68. K. Jacobs, Stochastic Processes for Physicists: Understanding Noisy Systems (Cambridge University Press, Cambridge, 2010).
  69. R. E. Kalman, A new approach to linear filtering and prediction problems, J. Basic Eng. 82, 35 (1960).
  70. R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, J. Basic Eng. 83, 95 (1961).
  71. R. Gurajala, P. B. Choppala, J. S. Meka, and P. D. Teal, Derivation of the Kalman filter in a Bayesian filtering perspective, in Proceedings of the 2021 2nd International Conference on Range Technology (ICORT) (IEEE, Piscataway, NJ, USA, 2021), pp. 1–5.
  72. V. Trees and L. Harry, Detection, Estimation, and Modulation Theory—Part I—Detection, Estimation, and Linear Modulation Theory (John Wiley & Sons, New York, NY, 2001).
  73. R. Gray, On the asymptotic eigenvalue distribution of Toeplitz matrices, IEEE Trans. Inf. Theory 18, 725 (1972).
  74. R. M. Gray et al., Toeplitz and circulant matrices: A review, Found. Trends® Commun. Inf. Theory 2, 155 (2006).
  75. M. Levin, Power spectrum parameter estimation, IEEE Trans. Inf. Theory 11, 100 (2003).
  76. P. Whittle, Hypothesis Testing in Time Series Analysis, Statistics (Uppsala Universitet, Statistiska Institutionen, Almqvist & Wiksells, Uppsala, 1951), Vol. 4.
  77. L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, A. Kugi, and M. Aspelmeyer, Real-time optimal quantum control of mechanical motion at room temperature, Nature (London) 595, 373 (2021).
  78. J. Liao et al., FPGA implementation of a Kalman-based motion estimator for levitated nanoparticles, IEEE Trans. Instrum. Meas. 68, 2374 (2018).
  79. F. Auger, M. Hilairet, J. M. Guerrero, E. Monmasson, T. Orlowska-Kowalska, and S. Katsura, Industrial applications of the Kalman filter: A review, IEEE Trans. Ind. Electron. 60, 5458 (2013).
  80. J. Ruiz-Rosero, G. Ramirez-Gonzalez, and R. Khanna, Field programmable gate array applications—A scientometric review, Computation 7, 63 (2019).
  81. M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013).
  82. M. H. Bitarafan and R. G. DeCorby, On-chip high-finesse Fabry-Perot microcavities for optical sensing and quantum information, Sensors 17, 1748 (2017).
  83. Zenodo's physical servers and technical infrastructure: CERN (the European Organization for Nuclear Research) in Geneva, Switzerland, https://doi.org/10.5281/zenodo.17259292.
  84. A. Böttcher and B. Silbermann, Introduction to Large Truncated Toeplitz Matrices (Springer Science & Business Media, 2012).
  85. A. Laub, A Schur method for solving algebraic Riccati equations, IEEE Trans. Autom. Control 24, 913 (1979).

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Phys. Rev. Research 8, 033038– Published 9 July, 2026
  • Received 3 October 2025
  • Accepted 10 June 2026
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