Abstract
In many communication scenarios, it is necessary to involve a third party for control and supervision. In the context of controlled bidirectional quantum secure direct communication (CBQSDC) protocols, the transmission of secret messages between two legitimate users is only permitted with the explicit permission of a controller. To address the issue of controlled communication, a CBQSDC protocol (CLYH2015) utilizing Bell states was proposed in the paper (Quant Inf Process 14, 3515–3522, 2015). Bell states have been widely recognized for their significance in the field of quantum secure direct communication. In a subsequent study published in (Quant Inf Process 16, 147, 2017), the research examined whether CLYH2015 protocol strictly requires the initial states to be Bell states. The conclusion drawn from this investigation is that CLYH2015 protocol working properly necessitates the use of Bell states as initial states. To explore alternative possibilities for the initial states in CLYH2015 protocol, a class of CBQSDC protocols employing the generalized Bell states (GBell states), \(a\arrowvert 00\rangle + b\arrowvert 11\rangle \), \({\bar{b}}\arrowvert 00\rangle -{\bar{a}}\arrowvert 11\rangle \), \(a\arrowvert 01\rangle + b\arrowvert 10\rangle \), and \({\bar{b}}\arrowvert 01\rangle -{\bar{a}}\arrowvert 10\rangle \), are designed where a and b are complex numbers with \(|a|=|b|=\frac{1}{\sqrt{2}}\), \({\bar{a}}\) and \({\bar{b}}\) the conjugate complex numbers of a and b, respectively. The class of designed CBQSDC protocols demonstrates several favorable properties, including resistance against information leakage, intercept-and-resend attacks, measure-resend attacks, as well as robustness against collective attacks. In addition, the unconditional security of the class of designed protocols is proved. Finally, to show the advantages of the class of designed protocols, they are compared with some with some previous closely associated protocols. Interestingly, it is worth noting that the Bell states can be considered a special case of the GBell states when both a and b are real numbers. Consequently, CLYH2015 protocol can be regarded as a particular instance of the designed CBQSDC protocols. This insight implies that the initial states in CLYH2015 protocol can be extended to include the GBell states, rather than being limited solely to the Bell states.
Similar content being viewed by others
Data availability statement
The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding authors.
References
Bennett,C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, pp. 175–179. IEEE, Bangalore India (1984)
Lo, H.-K., Chau, H.F.: Unconditional security of quantum key distribution over arbitrarily long distances. Science 283(5410), 2050–2056 (1999)
Gao, Z., Li, T., Li, Z.: Deterministic measurement-device-independent quantum secret sharing. Sci. China Phys. Mech. Astron. 63(12), 120311 (2020)
Dutta, A., Pathak, A.: Controlled secure direct quantum communication inspired scheme for quantum identity authentication. Quant. Inf. Process. 22(1), 13 (2022)
Long, G.-L., Liu, X.-S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65(3), 032302 (2002)
Deng, F.-G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)
Liu, X., Li, Z., Luo, D., Huang, C., Ma, D., Geng, M., Wang, J., Zhang, Z., Wei, K.: Practical decoy-state quantum secure direct communication. Sci. China Phys. Mech. Astron. 64(12), 120311 (2021)
Park, J., Kim, B., Heo, J.: Statistical fluctuation analysis for decoy-state quantum secure direct communication. Quantum Inf. Process. 22(2), 112 (2023)
Deng, F.-G., Long, G.L., Liu, X.-S.: Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68(4), 042317 (2003)
Li, T., Long, G.-L.: Quantum secure direct communication based on single-photon Bell-state measurement. New J. Phys. 22(6), 063017 (2020)
Sheng, Y.-B., Zhou, L., Long, G.-L.: One-step quantum secure direct communication. Sci. Bull. 67(4), 367–374 (2022)
Yang, C.-W., Lin, J., Wang, K.-L., Tsai, C.-W.: Cryptanalysis and improvement of a controlled quantum secure direct communication with authentication protocol based on five-particle cluster state. Quant. Inf. Process. 22(5), 196 (2023)
Guerra, A.G.D.A.H., Rios, F.F.S., Ramos, R.V.: Quantum secure direct communication of digital and analog signals using continuum coherent states. Quant. Inf. Process. 15, 4747–4758 (2016)
Chai, G., Cao, Z., Liu, W., Zhang, M., Liang, K., Peng, J.: Novel continuous-variable quantum secure direct communication and its security analysis. Laser Phys. Lett. 16(9), 095207 (2019)
Srikara, S., Chandrashekar, C.: Quantum direct communication protocols using discrete-time quantum walk. Quantum Inf. Process. 19, 1–15 (2020)
Cao, Z., Wang, L., Liang, K., Chai, G., Peng, J.: Continuous-variable quantum secure direct communication based on Gaussian mapping. Phys. Rev. Appl. 16(2), 024012 (2021)
Zhou, L., Sheng, Y.-B., Long, G.-L.: Device-independent quantum secure direct communication against collective attacks. Sci. Bull. 65(1), 12–20 (2020)
Zhou, L., Sheng, Y.-B.: One-step device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron. 65(5), 250311 (2022)
Zhou, L., Xu, B.-W., Zhong, W., Sheng, Y.-B.: Device-independent quantum secure direct communication with single-photon sources. Phys. Rev. Appl. 19(1), 014036 (2023)
Zhou, Z., Sheng, Y., Niu, P., Yin, L., Long, G., Hanzo, L.: Measurement-device-independent quantum secure direct communication. Sci. China Phys. Mech. Astron. 63(3), 1–6 (2020)
Ying, J.-W., Zhou, L., Zhong, W., Sheng, Y.-B.: Measurement-device-independent one-step quantum secure direct communication. Chin. Phys. B 31(12), 120303 (2022)
Das, N., Paul, G.: Measurement-device-independent quantum secure direct communication with user authentication. Quantum Inf. Process. 21(7), 260 (2022)
Hong, Y.-P., Zhou, L., Zhong, W., Sheng, Y.-B.: Measurement-device-independent three-party quantum secure direct communication. Quantum Inf. Process. 22(2), 111 (2023)
Nguyen, B.A.: Quantum dialogue. Phys. Lett. A 328(1), 6–10 (2004)
Man, Z.-X., Zhang, Z.-J., Li, Y.: Quantum dialogue revisited. Chin. Phys. Lett. 22(1), 22 (2005)
Xia, Y., Fu, C.-B., Zhang, S., Hong, S.-K., Yeon, K.-H., Um, C.-I.: Quantum dialogue by using the GHZ state. arXiv preprint arXiv:quant-ph/0601127 (2006)
Man, Z.-X., Xia, Y.-J., Zhang, Z.-J.: Secure deterministic bidirectional communication without entanglement. Int. J. Quantum Inf. 4(04), 739–746 (2006)
Yang, Y.-G., Wen, Q.-Y.: Quasi-secure quantum dialogue using single photons. Sci. China Ser. G Phys. Mech. Astron. 50(5), 558–562 (2007)
Tan, Y.-G., Cai, Q.-Y.: Classical correlation in quantum dialogue. Int. J. Quant. Inf. 6(02), 325–329 (2008)
Gao, F., Guo, F.-Z., Wen, Q.-Y., Zhu, F.-C.: Revisiting the security of quantum dialogue and bidirectional quantum secure direct communication. Sci. China Ser. G Phys. Mech. Astron. 51(5), 559–566 (2008)
Dong, L., Xiu, X.-M., Gao, Y.-J., Chi, F.: Quantum dialogue protocol using a class of three-photon W states. Commun. Theor. Phys. 52(5), 853 (2009)
Luo, Y.-P., Lin, C.-Y., Hwang, T.: Efficient quantum dialogue using single photons. Quant. Inf. Process. 13, 2451–2461 (2014)
Chang, Y., Zhang, S.-B., Yan, L.-L.: A bidirectional quantum secure direct communication protocol based on five-particle cluster state. Chin. Phys. Lett. 30(9), 090301 (2013)
Ye, T.-Y.: Fault-tolerant authenticated quantum dialogue using logical Bell states. Quant. Inf. Process. 14, 3499–3514 (2015)
Mohapatra, A.K., Balakrishnan, S.: Controller-independent bidirectional quantum direct communication. Quant. Inf. Process. 16, 1–11 (2017)
Chen, Y., Zou, X., Wang, X., Liu, J., Rong, Z., Huang, Z., Zheng, S., Liang, X., Wu, J.: Two intercept-and-resend attacks on a bidirectional quantum secure direct communication and its improvement. Quant. Inf. Process. 22, 346 (2023)
Srikanth, A., Balakrishnan, S.: Controller-independent quantum bidirectional communication using non-maximally entangled states. Quant. Inf. Process. 19, 1–11 (2020)
Ramachandran, M., Balakrishnan, S.: Effect of noise in the quantum bidirectional direct communication protocol using non-maximally entangled states. Int. J. Theor. Phys. 61(5), 127 (2022)
Qi, J.-M., Xu, G., Chen, X.-B., Wang, T.-Y., Cai, X.-Q., Yang, Y.-X.: Two authenticated quantum dialogue protocols based on three-particle entangled states. Quant. Inf. Process. 17, 1–19 (2018)
Li, W., Zha, X.-W., Yu, Y.: Secure quantum dialogue protocol based on four-qubit cluster state. Int. J. Theor. Phys. 57, 371–380 (2018)
Liu, Z., Chen, H.: Analyzing and improving the secure quantum dialogue protocol based on four-qubit cluster state. Int. J. Theor. Phys. 59, 2120–2126 (2020)
Chauhan, S., Gupta, N.: Bidirectional quantum secure direct communication using dense coding of four qubit cluster states. J. Sci. Res. 14(1), 179–187 (2022)
Man, Z.-X., Xia, Y.-J.: Controlled bidirectional quantum direct communication by using a GHZ state. Chin. Phys. Lett. 23(7), 1680 (2006)
Ye, T.-Y., Jiang, L.-Z.: Improvement of controlled bidirectional quantum direct communication using a GHZ state. Chin. Phys. Lett. 30(4), 040305 (2013)
Liu, Z.-H., Chen, H.-W.: Comment on “Improvement of controlled bidirectional quantum direct communication using a GHZ state”[Chin. Phys. Lett. 30 (2013) 040305]. Chinese Phys. Lett. 30(7), 079901 (2013)
Chang, C.-H., Luo, Y.-P., Yang, C.-W., Hwang, T.: Intercept-and-resend attack on controlled bidirectional quantum direct communication and its improvement. Quant. Inf. Process. 14, 3515–3522 (2015)
Pan, H.-M.: Controlled bidirectional quantum secure direct communication with six-qubit entangled states. Int. J. Theor. Phys. 60(8), 2943–2950 (2021)
Zou, X., Wang, X., Rong, Z., Huang, Z., Liu, J., Chen, Y.: Comment on “Controlled bidirectional quantum secure direct communication with six-qubit entangled states.” Int. J. Theoret. Phys. 62(2), 43 (2023)
Hu, J.-Y., Yu, B., Jing, M.-Y., Xiao, L.-T., Jia, S.-T., Qin, G.-Q., Long, G.-L.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5(9), e16144 (2016)
Zhu, F., Zhang, W., Sheng, Y., Huang, Y.: Experimental long-distance quantum secure direct communication. Sci. Bull. 62(22), 1519–1524 (2017)
Zhang, W., Ding, D.-S., Sheng, Y.-B., Zhou, L., Shi, B.-S., Guo, G.-C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118(22), 220501 (2017)
Sun, Z., Song, L., Huang, Q., Yin, L., Long, G., Lu, J., Hanzo, L.: Toward practical quantum secure direct communication: A quantum-memory-free protocol and code design. IEEE Trans. Commun. 68(9), 5778–5792 (2020)
Pan, D., Lin, Z., Wu, J., Zhang, H., Sun, Z., Ruan, D., Yin, L., Long, G.L.: Experimental free-space quantum secure direct communication and its security analysis. Photon. Res. 8(9), 1522–1531 (2020)
Qi, Z., Li, Y., Huang, Y., Feng, J., Zheng, Y., Chen, X.: A 15-user quantum secure direct communication network. Light Sci. Appl. 10(1), 183 (2021)
Zhang, H., Sun, Z., Qi, R., Yin, L., Long, G.-L., Lu, J.: Realization of quantum secure direct communication over 100 km fiber with time-bin and phase quantum states. Light Sci. Appl. 11(1), 83 (2022)
Liu, X., Luo, D., Lin, G., Chen, Z., Huang, C., Li, S., Zhang, C., Zhang, Z., Wei, K.: Fiber-based quantum secure direct communication without active polarization compensation. Sci. China Phys. Mech. Astron. 65(12), 120311 (2022)
Liu, J., Zou, X., Wang, X., Chen, Y., Rong, Z., Huang, Z., Zheng, S., Liang, X., Wu, J.: A class of general maximum entangled states and its applications in measurement-device-independent quantum secure direct communication. To appear
Yan, P.-S., Zhou, L., Zhong, W., Sheng, Y.-B.: Feasible measurement-based entanglement purification in linear optics. Opt. Express 29(6), 9363–9384 (2021)
Yan, P.-S., Zhou, L., Zhong, W., Sheng, Y.-B.: Feasible time-bin entanglement purification based on sum-frequency generation. Opt. Express 29(2), 571–583 (2021)
Yan, P.-S., Zhou, L., Zhong, W., Sheng, Y.-B.: Measurement-based logical qubit entanglement purification. Phys. Rev. A 105(6), 062418 (2022)
Yan, P.-S., Zhou, L., Zhong, W., Sheng, Y.-B.: Advances in quantum entanglement purification. Sci. China Phys. Mech. Astron. 66(5), 250301 (2023)
Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28(4), 656–715 (1949)
Wyner, A.D.: The wire-tap channel. Bell Syst. Tech. J. 54(8), 1355–1387 (1975)
Thangaraj, A., Dihidar, S., Calderbank, A.R., McLaughlin, S.W., Merolla, J.-M.: Applications of LDPC codes to the wiretap channel. IEEE Trans. Inf. Theory 53(8), 2933–2945 (2007)
Tyagi, H., Vardy, A.: Universal hashing for information-theoretic security. Proc. IEEE 103(10), 1781–1795 (2015)
Renner, R., Gisin, N., Kraus, B.: Information-theoretic security proof for quantum-key-distribution protocols. Phys. Rev. A 72(1), 012332 (2005)
Wu, J., Lin, Z., Yin, L., Long, G.-L.: Security of quantum secure direct communication based on Wyner’s wiretap channel theory. Quant. Eng. 1(4), 26 (2019)
Cabello, A.: Quantum key distribution in the Holevo limit. Phys. Rev. Lett. 85(26), 5635 (2000)
Pathak, A.: Efficient protocols for unidirectional and bidirectional controlled deterministic secure quantum communication: different alternative approaches. Quant. Inf. Process. 14, 2195–2210 (2015)
Acknowledgements
This work was supported in part by the Joint Research and Development Fund of Wuyi University, Hong Kong and Macao (No. 2021WGALH16), the National Natural Science Foundations of China (Nos. 61871205 and 11874312), the Innovation Program for Quantum Science and Technology (No. 2021ZD0302900), the Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515012623), the Innovation Project of Department of Education of Guangdong Province of China (No. 2017KTSCX180), the Science and Technology Project of Jiangmen City of China (No. 2021030101270004596), and Special Foundation in Key Fields for Universities of Guangdong Province (2023ZDZX4060).
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Competing Interests
The authors declare no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Liu, J., Zou, X., Wang, X. et al. Discussion on the initial states of controlled bidirectional quantum secure direct communication. Quantum Inf Process 22, 426 (2023). https://doi.org/10.1007/s11128-023-04178-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11128-023-04178-9