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  • Open Access

Catability as a Metric for Evaluating Superposed Coherent States

Šimon Bräuer*, Jan Provazník, Vojtěch Kala, and Petr Marek

  • Optics Department, Faculty of Science, Palacký University, 17. Listopadu 12, 77146 Olomouc, Czech Republic

  • *Contact author: brauer@optics.upol.cz
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Phys. Rev. Lett. 136, 090205 – Published 5 March, 2026

DOI: https://doi.org/10.1103/qfnt-6drh

Abstract

Superposed coherent states are central to quantum technologies, yet their reliable identification remains a challenge, especially in noisy or resource-constrained settings. We introduce a novel, directly measurable criterion for detecting catlike features in quantum states. The criterion is based on the concept of nonlinear squeezing and bypasses the need for full state tomography of the tested states. The numerical results confirm its robustness under loss and its potential for experimental implementation. The method naturally generalizes to more exotic superpositions, including multiheaded cat states.

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References (74)

  1. E. Schrödinger, Die Naturwiss. 23, 807 (1935).
  2. H. Jeong and M. S. Kim, Phys. Rev. A 65, 042305 (2002).
  3. T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, Phys. Rev. A 68, 042319 (2003).
  4. A. P. Lund, T. C. Ralph, and H. L. Haselgrove, Phys. Rev. Lett. 100, 030503 (2008).
  5. S.-W. Lee and H. Jeong, Phys. Rev. A 87, 022326 (2013).
  6. S. Omkar, Y. S. Teo, and H. Jeong, Phys. Rev. Lett. 125, 060501 (2020).
  7. S. Omkar, Y. S. Teo, S.-W. Lee, and H. Jeong, Phys. Rev. A 103, 032602 (2021).
  8. J. Hastrup and U. L. Andersen, Phys. Rev. Res. 4, 043065 (2022).
  9. J. Lee, N. Kang, S.-H. Lee, H. Jeong, L. Jiang, and S.-W. Lee, PRX Quantum 5, 030322 (2024).
  10. D. Su, I. Dhand, and T. C. Ralph, Phys. Rev. A 106, 042614 (2022).
  11. Z. Leghtas, G. Kirchmair, B. Vlastakis, R. J. Schoelkopf, M. H. Devoret, and M. Mirrahimi, Phys. Rev. Lett. 111, 120501 (2013).
  12. K. Duivenvoorden, B. M. Terhal, and D. Weigand, Phys. Rev. A 95, 012305 (2017).
  13. X. Pan, T. Krisnanda, A. Duina, K. Park, P. Song, C. Y. Fontaine, A. Copetudo, R. Filip, and Y. Y. Gao, PRX Quantum 6, 010304 (2025).
  14. A. P. Lund, H. Jeong, T. C. Ralph, and M. S. Kim, Phys. Rev. A 70, 020101(R) (2004).
  15. D. V. Sychev, A. E. Ulanov, A. A. Pushkina, M. W. Richards, I. A. Fedorov, and A. I. Lvovsky, Nat. Photonics 11, 379 (2017).
  16. D. J. Weigand and B. M. Terhal, Phys. Rev. A 97, 022341 (2018).
  17. M. Ježek, A. Tipsmark, R. Dong, J. Fiurášek, L. Mišta, R. Filip, and U. L. Andersen, Phys. Rev. A 86, 043813 (2012).
  18. M. Yukawa, K. Miyata, T. Mizuta, H. Yonezawa, P. Marek, R. Filip, and A. Furusawa, Opt. Express 21, 5529 (2013).
  19. M. Eaton, C. González-Arciniegas, R. N. Alexander, N. C. Menicucci, and O. Pfister, Quantum 6, 769 (2022).
  20. M. Endo, T. Nomura, T. Sonoyama, K. Takahashi, S. Takasu, D. Fukuda, T. Kashiwazaki, A. Inoue, T. Umeki, R. Nehra et al., arXiv:2502.08952.
  21. B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, Science 342, 607 (2013).
  22. N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang et al., Nature (London) 536, 441 (2016).
  23. X. L. He, Y. Lu, D. Q. Bao, H. Xue, W. B. Jiang, Z. Wang, A. F. Roudsari, P. Delsing, J. S. Tsai, and Z. R. Lin, Nat. Commun. 14, 6358 (2023).
  24. C. Monroe, D. M. Meekhof, B. E. King, and D. J. Wineland, Science 272, 1131 (1996).
  25. D. Kienzler, C. Flühmann, V. Negnevitsky, H.-Y. Lo, M. Marinelli, D. Nadlinger, and J. P. Home, Phys. Rev. Lett. 116, 140402 (2016).
  26. A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi et al., Science 365, 570 (2019).
  27. B. Hacker, S. Welte, S. Daiss, A. Shaukat, S. Ritter, L. Li, and G. Rempe, Nat. Photonics 13, 110 (2019).
  28. I. Shomroni, L. Qiu, and T. J. Kippenberg, Phys. Rev. A 101, 033812 (2020).
  29. B. D. Hauer, J. Combes, and J. D. Teufel, Phys. Rev. Lett. 130, 213604 (2023).
  30. R. Filip and L. Mišta, Phys. Rev. Lett. 106, 200401 (2011).
  31. M. Walschaers, PRX Quantum 2, 030204 (2021).
  32. L. Lachman and R. Filip, Prog. Quantum Electron. 83, 100395 (2022).
  33. C.-W. Lee and H. Jeong, Phys. Rev. Lett. 106, 220401 (2011).
  34. J. Fiurášek and M. Ježek, Phys. Rev. A 87, 062115 (2013).
  35. J. Park, J. Zhang, J. Lee, S.-W. Ji, M. Um, D. Lv, K. Kim, and H. Nha, Phys. Rev. Lett. 114, 190402 (2015).
  36. H. Kwon, C.-Y. Park, K. C. Tan, and H. Jeong, New J. Phys. 19, 043024 (2017).
  37. M. Bild, M. Fadel, Y. Yang, U. von Lüpke, P. Martin, A. Bruno, and Y. Chu, Science 380, 274 (2023).
  38. M. G. Genoni, M. L. Palma, T. Tufarelli, S. Olivares, M. S. Kim, and Matteo G. A. Paris, Phys. Rev. A 87, 062104 (2013).
  39. D. Stoler, Phys. Rev. D 1, 3217 (1970).
  40. E. Y. C. Lu, Lett. Al Nuovo Cimento Series 2 2, 1241 (1971).
  41. H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
  42. S. L. Braunstein, Phys. Rev. A 71, 055801 (2005).
  43. B. Yadin, F. C. Binder, J. Thompson, V. Narasimhachar, M. Gu, and M. S. Kim, Phys. Rev. X 8, 041038 (2018).
  44. C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Phys. Rev. Lett. 119, 170501 (2017).
  45. W. Jia, V. Xu, K. Kuns, M. Nakano, L. Barsotti, M. Evans, and N. Mavalvala (Members of the LIGO Scientific Collaboration), R. Abbott, I. Abouelfettouh et al., Science 385, 1318 (2024).
  46. D. Gottesman and J. Preskill, Phys. Rev. A 63, 022309 (2001).
  47. A. n. Oruganti, I. Derkach, R. Filip, and V. C. Usenko, Quantum Sci. Technol. 10, 025023 (2025).
  48. K. Park, R. Filip, P. Marek, and C. Oh, Phys. Rev. Appl. 18, 014060 (2022).
  49. S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998).
  50. A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, H. J. Kimble, and E. S. Polzik, Science 282, 706 (1998).
  51. Š. Bräuer, T. Opatrný, and P. Marek, Phys. Rev. Res. 7, 033176 (2025).
  52. V. Kala, J. Fadrný, M. Neset, J. Bílek, P. Marek, and M. Ježek, arXiv:2503.07574.
  53. K. Miyata, H. Ogawa, P. Marek, R. Filip, H. Yonezawa, J. I. Yoshikawa, and A. Furusawa, Phys. Rev. A 93, 022301 (2016).
  54. S. Konno, A. Sakaguchi, W. Asavanant, H. Ogawa, M. Kobayashi, P. Marek, R. Filip, J. I. Yoshikawa, and A. Furusawa, Phys. Rev. Appl. 15, 024024 (2021).
  55. Š. Bräuer and P. Marek, Opt. Express 29, 22648 (2021).
  56. V. Kala, R. Filip, and P. Marek, Opt. Express 30, 31456 (2022).
  57. P. Marek, Phys. Rev. Lett. 132, 210601 (2024).
  58. See Supplemental Material at http://link.aps.org/supplemental/10.1103/qfnt-6drh for additional figures, derivations, and footnotes.
  59. Š. Bräuer, J. Provazník, V. Kala, and P. Marek, Catability as a metric for evaluating superposed coherent states, GitHub repository https://github.com/jan-provaznik/catability.
  60. H. Le Jeannic, A. Cavaillès, K. Huang, R. Filip, and J. Laurat, Phys. Rev. Lett. 120, 073603 (2018).
  61. J. Provazník, P. Marek, J. Laurat, and R. Filip, Opt. Express 33, 16520 (2025).
  62. J. S. Ivan, K. K. Sabapathy, and R. Simon, Phys. Rev. A 84, 042311 (2011).
  63. A. Mari and J. Eisert, Phys. Rev. Lett. 109, 230503 (2012).
  64. H. Takahashi, K. Wakui, S. Suzuki, M. Takeoka, K. Hayasaka, A. Furusawa, and M. Sasaki, Phys. Rev. Lett. 101, 233605 (2008).
  65. K. Takase, J. I. Yoshikawa, W. Asavanant, M. Endo, and A. Furusawa, Phys. Rev. A 103, 013710 (2021).
  66. A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri, and P. Grangier, Nature (London) 448, 784 (2007).
  67. A. Laghaout, J. S. Neergaard-Nielsen, and U. L. Andersen, Opt. Commun. 337, 96 (2015).
  68. U. Chabaud, D. Markham, and F. Grosshans, Phys. Rev. Lett. 124, 063605 (2020).
  69. U. Chabaud, G. Roeland, M. Walschaers, F. Grosshans, V. Parigi, D. Markham, and N. Treps, PRX Quantum 2, 020333 (2021).
  70. J. Fiurášek, Opt. Express 30, 30630 (2022).
  71. J. Cohen, W. C. Smith, M. H. Devoret, and M. Mirrahimi, Phys. Rev. Lett. 119, 060503 (2017).
  72. C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith et al., Nature (London) 585, 357 (2020).
  73. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright et al., Nat. Methods 17, 261 (2020).
  74. J. D. Hunter, Comput. Sci. Eng. 9, 90 (2007).

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Phys. Rev. Lett. 136, 090205– Published 5 March, 2026
  • Received 3 July 2025
  • Revised 15 October 2025
  • Accepted 26 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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