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Exploiting higher-order correlation functions for photon-statistics-based characterization and reconstruction of arbitrary Gaussian states

Philip Heinzel1,* and René Sondenheimer1,2,†

  • *Contact author: philip.heinzel@uni-jena.de
  • †Contact author: rene.sondenheimer@uni-jena.de
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Phys. Rev. A 113, 013717 – Published 12 January, 2026

DOI: https://doi.org/10.1103/jgyv-dl9r

Abstract

Gaussian states are an essential building block for various applications in quantum optics and quantum information science, yet the precise relation between their second- and third-order correlation functions remains not fully explored. We discuss connections between these correlation functions by constructing an explicit decomposition formula for arbitrary sixth-order moments of ladder operators for general Gaussian states and demonstrate how the derived relations enable state classification from correlation data alone. Whereas violating these relations certifies non-Gaussianity, satisfying them provides evidence for a Gaussian-state description and allows a direct distinction among nondisplaced, nonsqueezed, and displaced-squeezed sectors of the Gaussian state space. Furthermore, we show that it is not possible to uniquely extract state parameters solely from correlation-function measurements without prior assumptions about the Gaussian state. Resolving this ambiguity requires additional loss-sensitive information, e.g., measuring the mean intensity or the vacuum overlap of each mode. In particular, we show under which circumstances these measurements can be used to reconstruct a generic Gaussian state.

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References (64)

  1. S. L. Braunstein and P. van Loock, Rev. Mod. Phys. 77, 513 (2005).
  2. G. Adesso and F. Illuminati, J. Phys. A: Math. Theor. 40, 7821 (2007).
  3. C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Rev. Mod. Phys. 84, 621 (2012).
  4. F. Grosshans and P. Grangier, Phys. Rev. Lett. 88, 057902 (2002).
  5. V. C. Usenko, L. Ruppert, and R. Filip, Phys. Rev. A 90, 062326 (2014).
  6. L. Ruppert, V. C. Usenko, and R. Filip, Phys. Rev. A 90, 062310 (2014).
  7. R. Filip, P. Marek, and U. L. Andersen, Phys. Rev. A 71, 042308 (2005).
  8. J. Zhao, H. Jeng, L. O. Conlon, S. Tserkis, B. Shajilal, K. Liu, T. C. Ralph, S. M. Assad, and P. K. Lam, Nat. Commun. 14, 4745 (2023).
  9. V. Roman-Rodriguez, D. Fainsin, G. L. Zanin, N. Treps, E. Diamanti, and V. Parigi, Phys. Rev. Res. 6, 043113 (2024).
  10. A. nag Oruganti, I. Derkach, R. Filip, and V. C. Usenko, Quantum Sci. Technol. 10, 025023 (2025).
  11. S.-H. Tan, B. I. Erkmen, V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, S. Pirandola, and J. H. Shapiro, Phys. Rev. Lett. 101, 253601 (2008).
  12. S. S. Y. Chua, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, Class. Quantum Grav. 31, 183001 (2014).
  13. H. Vahlbruch, M. Mehmet, K. Danzmann, and R. Schnabel, Phys. Rev. Lett. 117, 110801 (2016).
  14. R. Nichols, P. Liuzzo-Scorpo, P. A. Knott, and G. Adesso, Phys. Rev. A 98, 012114 (2018).
  15. L. McCuller, C. Whittle, D. Ganapathy, K. Komori, M. Tse, A. Fernandez-Galiana, L. Barsotti, P. Fritschel, M. MacInnis, F. Matichard, K. Mason, N. Mavalvala, R. Mittleman, H. Yu, M. E. Zucker, and M. Evans, Phys. Rev. Lett. 124, 171102 (2020).
  16. S. J. Lomonaco, Jr. and L. H. Kauffman, arXiv:quant-ph/0210141.
  17. C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Phys. Rev. Lett. 119, 170501 (2017).
  18. L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais, T. Vincent, J. F. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, A. E. Lita, T. Gerrits, S. W. Nam, V. D. Vaidya, M. Menotti, I. Dhand, Z. Vernon, N. Quesada, and J. Lavoie, Nature (London) 606, 75 (2022).
  19. S. Yu, Z.-P. Zhong, Y. Fang, R. B. Patel, Q.-P. Li, W. Liu, Z. Li, L. Xu, S. Sagona-Stophel, E. Mer, S. E. Thomas, Y. Meng, Z.-P. Li, Y.-Z. Yang, Z.-A. Wang, N.-J. Guo, W.-H. Zhang, G. K. Tranmer, Y. Dong, Y.-T. Wang, , Nat. Comput. Sci. 3, 839 (2023).
  20. A. L. Grimsmo and S. Puri, PRX Quantum 2, 020101 (2021).
  21. T. J. Sturges, T. McDermott, A. Buraczewski, W. R. Clements, J. J. Renema, S. W. Nam, T. Gerrits, A. Lita, W. S. Kolthammer, A. Eckstein, I. A. Walmsley, and M. Stobińska, npj Quantum Inf. 7, 91 (2021).
  22. X. Pan, J. Schwinger, N.-N. Huang, P. Song, W. Chua, F. Hanamura, A. Joshi, F. Valadares, R. Filip, and Y. Y. Gao, Phys. Rev. X 13, 021004 (2023).
  23. Z.-H. Li, F. Yu, Z.-Y. Li, M. Al-Amri, and M. S. Zubairy, Commun. Phys. 7, 134 (2024).
  24. A. Krstić, P. Tiwari, F. Höhe, F. Setzpfandt, U. Peschel, J. Ankerhold, and S. Saravi, Phys. Rev. Lett. 133, 203605 (2024).
  25. G. Yeoman and S. M. Barnett, J. Mod. Opt. 40, 1497 (1993).
  26. H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
  27. B. L. Schumaker and C. M. Caves, Phys. Rev. A 31, 3093 (1985).
  28. B. L. Schumaker, Phys. Rep. 135, 317 (1986).
  29. W.-M. Zhang, D. H. Feng, and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990).
  30. X. Ma and W. Rhodes, Phys. Rev. A 41, 4625 (1990).
  31. R. Simon, N. Mukunda, and B. Dutta, Phys. Rev. A 49, 1567 (1994).
  32. R. Simon, Phys. Rev. Lett. 84, 2726 (2000).
  33. L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000).
  34. J. Eisert and M. B. Plenio, Int. J. Quantum Inform. 01, 479 (2003).
  35. G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A 70, 022318 (2004).
  36. J. Eisert, S. Scheel, and M. B. Plenio, Phys. Rev. Lett. 89, 137903 (2002).
  37. A. Ferraro, S. Olivares, and M. G. A. Paris, arXiv:quant-ph/0503237.
  38. G. Vallone, G. Cariolaro, and G. Pierobon, Phys. Rev. A 99, 023817 (2019).
  39. J. B. Brask, arXiv:2102.05748.
  40. Y. Cardin and N. Quesada, Quantum 8, 1521 (2024).
  41. E. Fitzke, F. Niederschuh, and T. Walther, APL Photonics 8, 026106 (2023).
  42. J. Mizuno, K. Wakui, A. Furusawa, and M. Sasaki, Phys. Rev. A 71, 012304 (2005).
  43. M.-A. Lemonde, N. Didier, and A. A. Clerk, Phys. Rev. A 90, 063824 (2014).
  44. L. Bittel, F. A. Mele, J. Eisert, and A. A. Mele, arXiv:2508.14979.
  45. A. I. Lvovsky and M. G. Raymer, Rev. Mod. Phys. 81, 299 (2009).
  46. A. Christ, K. Laiho, A. Eckstein, K. N. Cassemiro, and C. Silberhorn, New J. Phys. 13, 033027 (2011).
  47. K. Wakui, Y. Eto, H. Benichi, S. Izumi, T. Yanagida, K. Ema, T. Numata, D. Fukuda, M. Takeoka, and M. Sasaki, Sci. Rep. 4, 4535 (2014).
  48. I. Gonoskov, R. Sondenheimer, C. Hünecke, D. Kartashov, U. Peschel, and S. Gräfe, arXiv:2211.06177.
  49. D. Theidel, V. Cotte, R. Sondenheimer, V. Shiriaeva, M. Froidevaux, V. Severin, A. Merdji-Larue, P. Mosel, S. Fröhlich, K.-A. Weber, U. Morgner, M. Kovacev, J. Biegert, and H. Merdji, PRX Quantum 5, 040319 (2024).
  50. D. Theidel, V. Cotte, P. Heinzel, H. Griguer, M. Weis, R. Sondenheimer, and H. Merdji arXiv:2411.02311.
  51. C. S. Lange, T. Hansen, and L. B. Madsen, Phys. Rev. A 109, 033110 (2024).
  52. J. Rivera-Dean, H. B. Crispin, P. Stammer, Th. Lamprou, E. Pisanty, M. Krüger, P. Tzallas, M. Lewenstein, and M. F. Ciappina, Phys. Rev. A 110, 063118 (2024).
  53. R. Glauber, Phys. Rev. 130, 2529 (1963).
  54. R. Loudon, The Quantum Theory of Light, 2nd ed. (Clarendon Press, Oxford, 1983).
  55. W. Vogel and D.-G. Welsch, Quantum Optics, 3rd ed. (Wiley-VCH, Weinheim, 2006).
  56. K. Laiho, T. Dirmeier, M. Schmidt, S. Reitzenstein, and C. Marquardt, Phys. Lett. A 435, 128059 (2022).
  57. L. Isserlis, Biometrika 12, 134 (1918).
  58. M. Houde, W. McCutcheon, and N. Quesada, Can. J. Phys. 102, 497 (2024).
  59. E. Callus, M. Gärttner, and T. Haas, Phys. Rev. A 112, 033704 (2025).
  60. S. Slussarenko and G. J. Pryde, Appl. Phys. Rev. 6, 041303 (2019).
  61. L. You, Nanophotonics 9, 2673 (2020).
  62. B.-m. Ann, Y. Song, J. Kim, D. Yang, and K. An, Phys. Rev. A 92, 023830 (2015).
  63. G. Sauer, M. Kolarczik, R. Gomez, J. Conrad, and F. Steinlechner, Resolving photon numbers using ultra-high-resolution timing of a single low-jitter superconducting nanowire detector, in Quantum 2.0 Conference and Exhibition (Optica Publishing Group, 2023), pp. QW4C.4.
  64. T. Schapeler, N. Lamberty, T. Hummel, F. Schlue, M. Stefszky, B. Brecht, C. Silberhorn, and T. J. Bartley, Phys. Rev. Appl. 22, 014024 (2024).

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Phys. Rev. A 113, 013717– Published 12 January, 2026
  • Received 24 October 2025
  • Accepted 18 December 2025
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