Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Quantum Tomography in Neutral Meson and Antimeson Systems

Kun Cheng*, Tao Han†, Matthew Low‡, and Tong Arthur Wu§

  • PITT PACC, Department of Physics and Astronomy, University of Pittsburgh, 3941 O’Hara Street, Pittsburgh, Pennsylvania 15260, USA

  • *Contact author: kun.cheng@pitt.edu
  • †Contact author: than@pitt.edu
  • ‡Contact author: mal431@pitt.edu
  • §Contact author: tow39@pitt.edu

Phys. Rev. Lett. 136, 181803 – Published 5 May, 2026

DOI: https://doi.org/10.1103/t9vg-hk6c

Abstract

The flavor space of particles produced in collider environments contains informative quantum correlations. We present a systematic approach for constructing the complete flavor density matrix for a meson and antimeson system (MM¯) in the Bloch vector space at a given time t, which can be at or after production. We point out that the Bs0 and K0 systems are superior to the Bd0 and D0 systems for quantum tomography because of their flavor oscillation and decay properties. Performing quantum tomography for the MM¯ system can facilitate the study of production mechanisms, decoherence phenomena, quantum information variables, and potential new sources of CP violation.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (90)

  1. M. Gell-Mann and A. Pais, Phys. Rev. 97, 1387 (1955).
  2. A. Apostolakis et al. (CPLEAR Collaboration), Phys. Lett. B 422, 339 (1998).
  3. F. Ambrosino et al. (KLOE Collaboration), Phys. Lett. B 642, 315 (2006).
  4. D. Babusci et al. (KLOE-2 Collaboration), J. High Energy Phys. 04 (2022) 059; 04 (2022) 169(E).
  5. A. Go (Belle Collaboration), J. Mod. Opt. 51, 991 (2004).
  6. A. Go et al. (Belle Collaboration), Phys. Rev. Lett. 99, 131802 (2007).
  7. J. Six, Phys. Lett. 114B, 200 (1982).
  8. F. Selleri, Lett. Nuovo Cimento 36, 521 (1983).
  9. P. H. Eberhard, Nucl. Phys. B398, 155 (1993).
  10. A. Di Domenico, Nucl. Phys. B450, 293 (1995).
  11. F. Uchiyama, Phys. Lett. A 231, 295 (1997).
  12. F. Selleri, Phys. Rev. A 56, 3493 (1997).
  13. R. Foadi and F. Selleri, Phys. Lett. B 461, 123 (1999).
  14. R. Foadi and F. Selleri, Phys. Rev. A 61, 012106 (2000).
  15. F. Benatti and R. Floreanini, Phys. Rev. D 57, R1332 (1998).
  16. F. Benatti and R. Floreanini, Eur. Phys. J. C 13, 267 (2000).
  17. R. A. Bertlmann, W. Grimus, and B. C. Hiesmayr, Phys. Rev. D 60, 114032 (1999).
  18. R. A. Bertlmann, W. Grimus, and B. C. Hiesmayr, Phys. Lett. A 289, 21 (2001).
  19. R. A. Bertlmann and B. C. Hiesmayr, Phys. Rev. A 63, 062112 (2001).
  20. R. A. Bertlmann, K. Durstberger, and B. C. Hiesmayr, Phys. Rev. A 68, 012111 (2003).
  21. R. A. Bertlmann, Lect. Notes Phys. 689, 1 (2006).
  22. J. Li and C.-F. Qiao, Phys. Rev. D 74, 076003 (2006).
  23. Y.-B. Ding, J.-l. Li, and C.-F. Qiao, High Energy Phys. Nucl. Phys. 31, 1086 (2007).
  24. A. Bramon and M. Nowakowski, Phys. Rev. Lett. 83, 1 (1999).
  25. B. Ancochea, A. Bramon, and M. Nowakowski, Phys. Rev. D 60, 094008 (1999).
  26. N. Gisin and A. Go, Am. J. Phys. 69, 264 (2001).
  27. R. H. Dalitz and G. Garbarino, Nucl. Phys. B606, 483 (2001).
  28. A. Bramon and G. Garbarino, Phys. Rev. Lett. 88, 040403 (2002).
  29. B. C. Hiesmayr, Found. Phys. Lett. 14, 231 (2001).
  30. A. Datta and D. Home, Phys. Lett. A 119, 3 (1986).
  31. A. Pompili and F. Selleri, Eur. Phys. J. C 14, 469 (2000).
  32. T. Ichikawa, S. Tamura, and I. Tsutsui, Phys. Lett. A 373, 39 (2008).
  33. K. Chen, Z.-P. Xing, and R. Zhu, Nucl. Phys. A1063, 123199 (2025).
  34. D. Atwood and A. Soni, Phys. Rev. D 82, 036003 (2010).
  35. S. Banerjee, A. K. Alok, and R. MacKenzie, Eur. Phys. J. Plus 131, 129 (2016).
  36. Y. Shi and J. Yang, Phys. Rev. D 98, 075019 (2018).
  37. Y. Shi and J.-C. Yang, Eur. Phys. J. C 80, 861 (2020).
  38. Y. Takubo, T. Ichikawa, S. Higashino, Y. Mori, K. Nagano, and I. Tsutsui, Phys. Rev. D 104, 056004 (2021).
  39. M. Fabbrichesi, R. Floreanini, E. Gabrielli, and L. Marzola, Phys. Rev. D 112, L091301 (2025).
  40. A. J. Leggett and A. Garg, Phys. Rev. Lett. 54, 857 (1985).
  41. J. Naikoo and S. Banerjee, Eur. Phys. J. C 78, 602 (2018).
  42. J. Naikoo, A. K. Alok, and S. Banerjee, Phys. Rev. D 97, 053008 (2018).
  43. M. Blasone, F. Illuminati, L. Petruzziello, K. Simonov, and L. Smaldone, Phys. Rev. A 109, 062209 (2024).
  44. R. von Kuk, K. Lee, J. K. L. Michel, and Z. Sun, arXiv:2503.22607.
  45. F. Bloch, Phys. Rev. 70, 460 (1946).
  46. R. P. Feynman, J. Vernon, Frank L., and R. W. Hellwarth, J. Appl. Phys. 28, 49 (1957).
  47. P. Caban, J. Rembielinski, K. A. Smolinski, Z. Walczak, and M. Wlodarczyk, Phys. Lett. A 357, 6 (2006).
  48. F. Roccati, G. M. Palma, F. Bagarello, and F. Ciccarello, Open Syst. Inf. Dyn. 29, 2250004 (2022).
  49. D. Karamitros, T. McKelvey, and A. Pilaftsis, Phys. Rev. D 108, 016006 (2023); 109, 059901(E) (2024).
  50. A. K. Alok, S. Banerjee, N. R. S. Chundawat, and S. U. Sankar, J. High Energy Phys. 05 (2024) 124.
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/t9vg-hk6c for a detailed derivation of the time evolution of meson systems.
  52. B. O. Kerbikov, Nucl. Phys. A975, 59 (2018).
  53. D. Karamitros, T. McKelvey, and A. Pilaftsis, Phys. Rev. D 111, 096020 (2025).
  54. U. Fano, Rev. Mod. Phys. 55, 855 (1983).
  55. R. F. Werner, Phys. Rev. A 40, 4277 (1989).
  56. R. Aaij et al. (LHCb Collaboration), Nat. Phys. 18, 1 (2022).
  57. A. Apostolakis et al. (CPLEAR Collaboration), Phys. Lett. B 458, 545 (1999).
  58. C. Oswald and T. K. Pedlar, Mod. Phys. Lett. A 28, 1330036 (2013).
  59. J. Bernabeu and A. Di Domenico, Phys. Rev. D 105, 116004 (2022).
  60. D. Babusci et al. (KLOE-2 Collaboration), Phys. Lett. B 845, 138164 (2023).
  61. R. Glattauer, Proc. Sci. EPS-HEP2015 (2015) 554.
  62. R. Louvot et al. (Belle Collaboration), Phys. Rev. Lett. 102, 021801 (2009).
  63. D. d’Enterria and A. M. Snigirev, Phys. Rev. Lett. 118, 122001 (2017).
  64. R. Aaij et al. (LHCb Collaboration), Phys. Rev. D 100, 031102 (2019).
  65. Y. Afik, Y. Kats, J. R. M. n. de Nova, A. Soffer, and D. Uzan, Phys. Rev. D 111, L111902 (2025).
  66. A. Di Domenico, Symmetry 12, 2063 (2020).
  67. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
  68. J. S. Bell, Phys. Phys. Fiz. 1, 195 (1964).
  69. W. Zurek, Ann. Phys. (Berlin) 512, 855 (2000).
  70. H. Ollivier and W. H. Zurek, Phys. Rev. Lett. 88, 017901 (2001).
  71. M. Horodecki, J. Oppenheim, and A. Winter, Nature (London) 436, 673 (2005).
  72. L. Leone, S. F. E. Oliviero, and A. Hamma, Phys. Rev. Lett. 128, 050402 (2022).
  73. Y. Afik and J. R. M. de Nova, Eur. Phys. J. Plus 136, 907 (2021).
  74. A. J. Barr, Phys. Lett. B 825, 136866 (2022).
  75. M. Fabbrichesi, R. Floreanini, and G. Panizzo, Phys. Rev. Lett. 127, 161801 (2021).
  76. C. Severi, C. D. E. Boschi, F. Maltoni, and M. Sioli, Eur. Phys. J. C 82, 285 (2022).
  77. M. Genovese, C. Novero, and E. Predazzi, Phys. Lett. B 513, 401 (2001).
  78. M. Genovese, C. Novero, and E. Predazzi, Found. Phys. 32, 589 (2002).
  79. A. Bramon and G. Garbarino, Phys. Rev. Lett. 89, 160401 (2002).
  80. M. Genovese, Phys. Rev. A 69, 022103 (2004).
  81. R. A. Bertlmann, A. Bramon, G. Garbarino, and B. C. Hiesmayr, Phys. Lett. A 332, 355 (2004).
  82. A. Bramon, R. Escribano, and G. Garbarino, J. Mod. Opt. 52, 1681 (2005).
  83. A. Bramon, R. Escribano, and G. Garbarino, Found. Phys. 36, 563 (2006).
  84. M. Genovese, Eur. Phys. J. C 42, 25 (2005).
  85. W. K. Wootters, Phys. Rev. Lett. 80, 2245 (1998).
  86. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).
  87. S. Luo, Phys. Rev. A 77, 042303 (2008).
  88. T. Han, M. Low, N. McGinnis, and S. Su, J. High Energy Phys. 05 (2025) 081.
  89. S. Jevtic, M. J. W. Hall, M. R. Anderson, M. Zwierz, and H. M. Wiseman, J. Opt. Soc. Am. B 32, A40 (2015).
  90. N. Friis, S. Bulusu, and R. Bertlmann, J. Phys. A 50, 125301 (2017).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation