- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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

Collective Randomized Measurements in Quantum Information Processing

Satoya Imai1,2, Géza Tóth3,4,5,6,7, and Otfried Gühne1

PDF

Phys. Rev. Lett. 133, 060203 – Published 8 August, 2024

DOI: https://doi.org/10.1103/PhysRevLett.133.060203

Abstract

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (121)

  1. A. Elben, S. T. Flammia, H.-Y. Huang, R. Kueng, J. Preskill, B. Vermersch, and P. Zoller, Nat. Rev. Phys. 5, 9 (2023).
  2. P. Cieśliński, S. Imai, J. Dziewior, O. Gühne, L. Knips, W. Laskowski, J. Meinecke, T. Paterek, and T. Vértesi, arXiv:2307.01251.
  3. T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, and C. F. Roos, Science 364, 260 (2019).
  4. A. Elben, B. Vermersch, M. Dalmonte, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 120, 050406 (2018).
  5. A. Ketterer, N. Wyderka, and O. Gühne, Phys. Rev. Lett. 122, 120505 (2019).
  6. S. Imai, N. Wyderka, A. Ketterer, and O. Gühne, Phys. Rev. Lett. 126, 150501 (2021).
  7. Z. Liu, Y. Tang, H. Dai, P. Liu, S. Chen, and X. Ma, Phys. Rev. Lett. 129, 260501 (2022).
  8. N. Wyderka and A. Ketterer, PRX Quantum 4, 020325 (2023).
  9. S. Liu, Q. He, M. Huber, O. Gühne, and G. Vitagliano, PRX Quantum 4, 020324 (2023).
  10. N. Wyderka, A. Ketterer, S. Imai, J. L. Bönsel, D. E. Jones, B. T. Kirby, X.-D. Yu, and O. Gühne, Phys. Rev. Lett. 131, 090201 (2023).
  11. M. C. Tran, B. Dakić, F. Arnault, W. Laskowski, and T. Paterek, Phys. Rev. A 92, 050301(R) (2015).
  12. M. C. Tran, B. Dakić, W. Laskowski, and T. Paterek, Phys. Rev. A 94, 042302 (2016).
  13. A. Ketterer, N. Wyderka, and O. Gühne, Quantum 4, 325 (2020).
  14. L. Knips, J. Dziewior, W. Kłobus, W. Laskowski, T. Paterek, P. J. Shadbolt, H. Weinfurter, and J. D. Meinecke, npj Quantum Inf. 6, 51 (2020).
  15. A. Ketterer, S. Imai, N. Wyderka, and O. Gühne, Phys. Rev. A 106, L010402 (2022).
  16. Z. Liu, P. Zeng, Y. Zhou, and M. Gu, Phys. Rev. A 105, 022407 (2022).
  17. S. J. van Enk and C. W. J. Beenakker, Phys. Rev. Lett. 108, 110503 (2012).
  18. A. Elben, B. Vermersch, C. F. Roos, and P. Zoller, Phys. Rev. A 99, 052323 (2019).
  19. A. Elben, B. Vermersch, R. van Bijnen, C. Kokail, T. Brydges, C. Maier, M. K. Joshi, R. Blatt, C. F. Roos, and P. Zoller, Phys. Rev. Lett. 124, 010504 (2020).
  20. B. Vermersch, A. Elben, L. M. Sieberer, N. Y. Yao, and P. Zoller, Phys. Rev. X 9, 021061 (2019).
  21. A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, and B. Vermersch, Sci. Adv. 6, eaaz3666 (2020).
  22. Z.-P. Cian, H. Dehghani, A. Elben, B. Vermersch, G. Zhu, M. Barkeshli, P. Zoller, and M. Hafezi, Phys. Rev. Lett. 126, 050501 (2021).
  23. B. Vermersch, A. Rath, B. Sundar, C. Branciard, J. Preskill, and A. Elben, PRX Quantum 5, 010352 (2024).
  24. M. Yu, D. Li, J. Wang, Y. Chu, P. Yang, M. Gong, N. Goldman, and J. Cai, Phys. Rev. Res. 3, 043122 (2021).
  25. A. Rath, C. Branciard, A. Minguzzi, and B. Vermersch, Phys. Rev. Lett. 127, 260501 (2021).
  26. V. Vitale, A. Rath, P. Jurcevic, A. Elben, C. Branciard, and B. Vermersch, arXiv:2307.16882.
  27. A. Elben, R. Kueng, H.-Y. R. Huang, R. van Bijnen, C. Kokail, M. Dalmonte, P. Calabrese, B. Kraus, J. Preskill, P. Zoller et al., Phys. Rev. Lett. 125, 200501 (2020).
  28. Y. Zhou, P. Zeng, and Z. Liu, Phys. Rev. Lett. 125, 200502 (2020).
  29. X.-D. Yu, S. Imai, and O. Gühne, Phys. Rev. Lett. 127, 060504 (2021).
  30. A. Neven, J. Carrasco, V. Vitale, C. Kokail, A. Elben, M. Dalmonte, P. Calabrese, P. Zoller, B. Vermersch, R. Kueng et al., npj Quantum Inf. 7, 152 (2021).
  31. V. Vitale, A. Elben, R. Kueng, A. Neven, J. Carrasco, B. Kraus, P. Zoller, P. Calabrese, B. Vermersch, and M. Dalmonte, SciPost Phys. 12, 106 (2022).
  32. J. Carrasco, M. Votto, V. Vitale, C. Kokail, A. Neven, P. Zoller, B. Vermersch, and B. Kraus, Phys. Rev. A 109, 012422 (2024).
  33. S. Aaronson, in Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing (2018), pp. 325–338, 10.1145/3188745.3188802.
  34. H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020).
  35. T. Zhang, J. Sun, X.-X. Fang, X.-M. Zhang, X. Yuan, and H. Lu, Phys. Rev. Lett. 127, 200501 (2021).
  36. G. I. Struchalin, Y. A. Zagorovskii, E. V. Kovlakov, S. S. Straupe, and S. P. Kulik, PRX Quantum 2, 010307 (2021).
  37. H. C. Nguyen, J. L. Bönsel, J. Steinberg, and O. Gühne, Phys. Rev. Lett. 129, 220502 (2022).
  38. A. Rath, V. Vitale, S. Murciano, M. Votto, J. Dubail, R. Kueng, C. Branciard, P. Calabrese, and B. Vermersch, PRX Quantum 4, 010318 (2023).
  39. J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, Phys. Rev. Lett. 83, 1319 (1999).
  40. V. Meyer, M. A. Rowe, D. Kielpinski, C. A. Sackett, W. M. Itano, C. Monroe, and D. J. Wineland, Phys. Rev. Lett. 86, 5870 (2001).
  41. M. Kitagawa and M. Ueda, Phys. Rev. A 47, 5138 (1993).
  42. D. J. Wineland, J. J. Bollinger, W. M. Itano, and D. J. Heinzen, Phys. Rev. A 50, 67 (1994).
  43. A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London) 409, 63 (2001).
  44. G. Tóth, C. Knapp, O. Gühne, and H. J. Briegel, Phys. Rev. Lett. 99, 250405 (2007).
  45. G. Tóth, C. Knapp, O. Gühne, and H. J. Briegel, Phys. Rev. A 79, 042334 (2009).
  46. J. Ma, X. Wang, C.-P. Sun, and F. Nori, Phys. Rep. 509, 89 (2011).
  47. L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Rev. Mod. Phys. 90, 035005 (2018).
  48. D. Braun, G. Adesso, F. Benatti, R. Floreanini, U. Marzolino, M. W. Mitchell, and S. Pirandola, Rev. Mod. Phys. 90, 035006 (2018).
  49. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
  50. C. Dankert, M. Math. thesis, University of Waterloo, 2005, arXiv:quant-ph/0512217.
  51. D. Gross, K. Audenaert, and J. Eisert, J. Math. Phys. (N.Y.) 48, 052104 (2007).
  52. K. Van Kirk, J. Cotler, H.-Y. Huang, and M. D. Lukin, arXiv:2212.06084.
  53. N. Friis, G. Vitagliano, M. Malik, and M. Huber, Nat. Rev. Phys. 1, 72 (2019).
  54. G. Tóth and O. Gühne, Phys. Rev. Lett. 102, 170503 (2009).
  55. K. Eckert, J. Schliemann, D. Bruß, and M. Lewenstein, Ann. Phys. (Amsterdam) 299, 88 (2002).
  56. J. K. Stockton, J. M. Geremia, A. C. Doherty, and H. Mabuchi, Phys. Rev. A 67, 022112 (2003).
  57. J. A. Miszczak, Z. Puchała, P. Horodecki, A. Uhlmann, and K. Życzkowski, arXiv:0805.2037.
  58. T. Ichikawa, T. Sasaki, I. Tsutsui, and N. Yonezawa, Phys. Rev. A 78, 052105 (2008).
  59. T.-C. Wei, Phys. Rev. A 81, 054102 (2010).
  60. K. Hansenne, Z.-P. Xu, T. Kraft, and O. Gühne, Nat. Commun. 13, 496 (2022).
  61. D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Phys. Rev. A 46, R6797 (1992).
  62. X. Wang and B. C. Sanders, Phys. Rev. A 68, 012101 (2003).
  63. J. K. Korbicz, J. I. Cirac, and M. Lewenstein, Phys. Rev. Lett. 95, 120502 (2005).
  64. J. K. Korbicz, O. Gühne, M. Lewenstein, H. Häffner, C. F. Roos, and R. Blatt, Phys. Rev. A 74, 052319 (2006).
  65. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.133.060203 for the appendices, which include Refs. [66–80].
  66. G. Kimura, Phys. Lett. A 314, 339 (2003).
  67. R. A. Bertlmann and P. Krammer, J. Phys. A 41, 235303 (2008).
  68. C. Eltschka and J. Siewert, Quantum 2, 64 (2018).
  69. L. Wei, Z. Jia, D. Kaszlikowski, and S. Tan, arXiv:2202.10989.
  70. G. Vitagliano, P. Hyllus, I. L. Egusquiza, and G. Tóth, Phys. Rev. Lett. 107, 240502 (2011).
  71. G. Vitagliano, I. Apellaniz, I. L. Egusquiza, and G. Tóth, Phys. Rev. A 89, 032307 (2014).
  72. L. Zhang, arXiv:1408.3782.
  73. D. A. Roberts and B. Yoshida, J. High Energy Phys. 04 (2017) 121.
  74. R. J. Garcia, Y. Zhou, and A. Jaffe, Phys. Rev. Res. 3, 033155 (2021).
  75. F. G. S. L. Brandão, W. Chemissany, N. Hunter-Jones, R. Kueng, and J. Preskill, PRX Quantum 2, 030316 (2021).
  76. S. Imai, O. Gühne, and S. Nimmrichter, Phys. Rev. A 107, 022215 (2023).
  77. L. Mirsky, Monatshefte fur Mathematik 79, 303 (1975).
  78. G. Tóth, J. Opt. Soc. Am. B 24, 275 (2007).
  79. J. L. Bönsel, S. Imai, Y.-C. Liu, and O. Gühne, arXiv:2311.17845.
  80. B. O’Neill, Am. Stat. 68, 282 (2014).
  81. A. U. Devi, M. Uma, R. Prabhu, and A. Rajagopal, Phys. Lett. A 364, 203 (2007).
  82. F. Bohnet-Waldraff, D. Braun, and O. Giraud, Phys. Rev. A 94, 042343 (2016).
  83. G. Tóth, Phys. Rev. A 69, 052327 (2004).
  84. B. Collins, S. Matsumoto, and J. Novak, Not. Am. Math. Soc. 69, 734 (2022).
  85. P. D. Seymour and T. Zaslavsky, Adv. Math. 52, 213 (1984).
  86. T. Eggeling and R. F. Werner, Phys. Rev. A 63, 042111 (2001).
  87. G. Tóth and M. W. Mitchell, New J. Phys. 12, 053007 (2010).
  88. I. Urizar-Lanz, P. Hyllus, I. L. Egusquiza, M. W. Mitchell, and G. Tóth, Phys. Rev. A 88, 013626 (2013).
  89. N. Behbood, F. M. Ciurana, G. Colangelo, M. Napolitano, G. Tóth, R. J. Sewell, and M. W. Mitchell, Phys. Rev. Lett. 113, 093601 (2014).
  90. J. Kong, R. Jiménez-Martínez, C. Troullinou, V. G. Lucivero, G. Tóth, and M. W. Mitchell, Nat. Commun. 11, 2415 (2020).
  91. A. Peres, Phys. Rev. Lett. 77, 1413 (1996).
  92. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Lett. A 283, 1 (2001).
  93. I. Frérot and T. Roscilde, Phys. Rev. Lett. 126, 140504 (2021).
  94. G. Müller-Rigat, A. Aloy, M. Lewenstein, and I. Frérot, PRX Quantum 2, 030329 (2021).
  95. G. Tóth, Phys. Rev. A 85, 022322 (2012).
  96. P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, and A. Smerzi, Phys. Rev. A 85, 022321 (2012).
  97. G. Tóth and I. Apellaniz, J. Phys. A 47, 424006 (2014).
  98. G. Tóth, W. Wieczorek, R. Krischek, N. Kiesel, P. Michelberger, and H. Weinfurter, New J. Phys. 11, 083002 (2009).
  99. P. Krammer, H. Kampermann, D. Bruß, R. A. Bertlmann, L. C. Kwek, and C. Macchiavello, Phys. Rev. Lett. 103, 100502 (2009).
  100. A. Chiuri, G. Vallone, N. Bruno, C. Macchiavello, D. Bruß, and P. Mataloni, Phys. Rev. Lett. 105, 250501 (2010).
  101. M. Cramer, M. B. Plenio, and H. Wunderlich, Phys. Rev. Lett. 106, 020401 (2011).
  102. O. Marty, M. Epping, H. Kampermann, D. Bruß, M. B. Plenio, and M. Cramer, Phys. Rev. B 89, 125117 (2014).
  103. M. Borrelli, M. Rossi, C. Macchiavello, and S. Maniscalco, Phys. Rev. A 90, 020301(R) (2014).
  104. O. Marty, M. Cramer, G. Vitagliano, G. Toth, and M. B. Plenio, arXiv:1708.06986.
  105. Z. Li, Y.-G. Han, H.-F. Sun, J. Shang, and H. Zhu, Phys. Rev. A 103, 022601 (2021).
  106. J. Steinberg and O. Gühne, arXiv:2210.13475.
  107. K. R. Parthasarathy, Proc. Math. Sci. 114, 365 (2004).
  108. M. Demianowicz and R. Augusiak, Phys. Rev. A 98, 012313 (2018).
  109. K. Lange, J. Peise, B. Lücke, I. Kruse, G. Vitagliano, I. Apellaniz, M. Kleinmann, G. Tóth, and C. Klempt, Science 360, 416 (2018).
  110. M. Fadel, T. Zibold, B. Décamps, and P. Treutlein, Science 360, 409 (2018).
  111. P. Kunkel, M. Prüfer, H. Strobel, D. Linnemann, A. Frölian, T. Gasenzer, M. Gärttner, and M. K. Oberthaler, Science 360, 413 (2018).
  112. D. Shin, B. Henson, S. Hodgman, T. Wasak, J. Chwedeńczuk, and A. Truscott, Nat. Commun. 10, 4447 (2019).
  113. M. Fadel, B. Yadin, Y. Mao, T. Byrnes, and M. Gessner, New J. Phys. 25, 073006 (2023).
  114. G. Vitagliano, M. Fadel, I. Apellaniz, M. Kleinmann, B. Lücke, C. Klempt, and G. Tóth, Quantum 7, 914 (2023).
  115. J. Kofler and Č. Brukner, Phys. Rev. A 74, 050304(R) (2006).
  116. M. Gessner, A. Smerzi, and L. Pezzè, Phys. Rev. Lett. 122, 090503 (2019).
  117. J. Tura, R. Augusiak, A. B. Sainz, T. Vértesi, M. Lewenstein, and A. Acín, Science 344, 1256 (2014).
  118. J. Tura, R. Augusiak, A. B. Sainz, B. Lücke, C. Klempt, M. Lewenstein, and A. Acín, Ann. Phys. (Amsterdam) 362, 370 (2015).
  119. S. Wagner, R. Schmied, M. Fadel, P. Treutlein, N. Sangouard, and J.-D. Bancal, Phys. Rev. Lett. 119, 170403 (2017).
  120. J. Guo, J. Tura, Q. He, and M. Fadel, Phys. Rev. Lett. 131, 070201 (2023).
  121. O. Gühne and G. Tóth, Phys. Rep. 474, 1 (2009).

Outline

Information

Phys. Rev. Lett. 133, 060203– Published 8 August, 2024
  • Received 1 November 2023
  • Revised 8 May 2024
  • Accepted 9 July 2024
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation