Article Sidebar
Date Published:
23/06/2024
Online Published:
23/06/2024
Online Published:
21/05/2024
Abstract Views: 47
Views PDF: 36
Views PDF: 36
Section
Articles
How to Cite
Nguyen Ba, A. (2024). Secure direct message exchange based on simultaneous usage of two different degrees of freedom. Thang Long Journal of Science: Mathematics and Mathematical Sciences, 3(1). https://science.thanglong.edu.vn/index.php/volc/article/view/125
Secure direct message exchange based on simultaneous usage of two different degrees of freedom
Main Article Content
Abstract
In the era of information explosion supplied with a veryhigh level of technology as of today, the loss or leakage of information is one of the most severe problems. Security in communication has thus become more important than ever. In this paper, two protocols for quantum secure direct exchange of messages are proposed using hyperentangled photon pairs as resource for exchanging informative bits and single photons in hyperstates as resource for detecting eavesdroppers. In both the protocols the photons need to be transmitted only once from one to the other communicating party. However, the ways to transmit photons are different in the two proposed protocols. The first protocol employs block transmission of photons. Although its security is unconditional, it compulsorily requires quantum memories at both communicating stations. Contrasting to the first protocol, in the second protocol single photons are transmitted one by one and subject to immediate processing without the need of any quantum memories. The security of the second protocol is asymptotic in the sense that the chance for eavesdroppers to pass is approaching zero in the limit of long messages. Comparison with other protocols is also given.
Article Details
Keywords
Secure direct message exchange, P-DOF, S-DOF, hyperentanglement, hyperstate
References
[1] Rivest R., Shamir A. and Adleman L., A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM 21 (1978), 120.
[2] Shor P. W., Algorithms for Quantum Computation: Discrete Logarithms and Factoring. Proc. 35th Annual Symposium on Foundations of ComputerScience. IEEE Comput. Soc. Press. (1994) 124
[3] Bennett C. H. and Brassard G., Quantum Cryptography: Public Key Distribution and Coin Tossing. Proc. IEEE Int. Conf. Computers, Systems, and Signal Processing (Bangalore) (1984) 175.
[4] Ekert A. K., Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67 (1991) 661.
[5] Bennett C. H., Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68 (1992) 3121.
[6] Shannon C., Communication theory of secrecy systems. Bell System Technical Journal 28 (1949) 656.
[7] Bostrom K. and Felbinger T. F., Deterministic Secure Direct Communication Using Entanglement. Phys. Rev. Lett. 89 (2002) 187902.
[8] Beige A., Englerta B. G., Kurtsieferc Ch.and Weinfurter H., Secure communication with a publicly known key. Acta Phys. Pol. A 101 (2002) 357.
[9] Deng F. G., Long G. L. and Liu X. S., Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68 (2003) 042317.
[10] Deng F. G. and Long G. L., Secure direct communication with a quantum one-time pad. Phys. Rev. A 69 (2004) 052319.
[11] Li X. H., Zhou P., Liang Y. J., Li C. Y., Zhou H. Y. and Deng F. G., Quantum Secure Direct Communication Network with Two-Step Protocol. Chin. Phys. Lett. 23 (2006) 1080.
[12] Hu J. Y., Yu B., Jing M. Y., Xiao L. T., Jia S. T., Qin G. Q. and Long G. L., Experimental quantum secure direct communication with single photons. Light: Sci. & Appl. 5 (2016) e16144.
[13] Zhang W., Ding D. S., Sheng Y. B., Zhou L., Shi B. S. and Guo G. C., Quantum Secure Direct Communication with Quantum Memory. Phys. Rev. Lett. 118 (2017) 220501.
[14] Zhu F., Zhang W., Sheng Y. B. and Huang Y. D., Experimental long-distance quantum secure direct communication. Sci. Bull. 62 (2017) 1519.
[15] Pan D., Lin Z. S., Wu J. W., Zhang H. R., Sun Z., Ruan D., Yin L. G. and Long G. L., Experimental free-space quantum secure direct communication and its security analysis. Photon. Res. 8 (2020) 1522.
[16] Srikara S., Thapliyal K. and Pathak A., Continuous variable direct secure quantum communication using Gaussian states. Quant. Inf. Process. 19 (2020) 132.
[17] Nayana D. and Goutam P., Cryptanalysis of quantum secure direct communication protocol with mutual authentication based on single photons and Bell states. Europhys. Lett. 138 (2022) 48001. Secure direct message exchange ... 17
[18] Zhang H. R., Sun Z., Qi R. Y., Yin L. G., Long G. L. and Lu J. H., Realization of quantum secure direct communication over 100 km fiber with time-bin and phase quantum states. Light Sci. & Appl. 11 (2022) 83.
[19] Pan D., Song X. T. and Long G. L., Free-space quantum secure direct communication: basics, progress, and outlook. Advanced Devices & Instrunentation 4 (2023) 0004.
[20] Panda S. S., Yasir P. A. A. and Chandrashekar C. M., Quantum direct communication protocol using recurrence in k-cycle quantum walks. Phys. Rev. A 107 (2023) 022611.
[21] Nguyen B. A., Quantum dialogue. Phys. Lett. A 328 (2004) 6.
[22] Nguyen B. A., Secure dialogue without a prior key distribution. J. Kor. Phys. Soc. 47 (2005) 562.
[23] Yan C., Man Z. X. and Xia Y. J., Quantum Bidirectional Secure Direct Communication via Entanglement Swapping. Chin. Phys. Lett. 24(2007) 19.
[24] Shi G. F., Xi X. Q. and Tian X. L., Bidirectional quantum securecommunication based on a shared private Bell state. Opt. Commun. 282(2009) 2460.
[25] Shan C. J., Liu J. B., Cheng W. W., Liu T. K., Huang Y. X. and Li H., Bidirectional quantum secure direct communication in drivencavity QED. Mod. Phys. Lett. B 23 (2009) 3225.
[26] Shi G. F., Xi X. Q. and Hu M. L., Quantum secure dialogue by usingsingle photons. Opt. Commun. 283 (2010) 1984.
[27] Gao G., Two quantum dialogue protocols without information leakage. Opt. Commun. 283 (2010) 2288.
[28] Shi G. F., Bidirectional quantum secure communication scheme based on Bell states and auxiliary particles. Opt. Commun. 283 (2010) 5275.
[29] Pathak A., Efficient protocols for unidirectional and bidirectional controlled deterministic secure quantum communication: different alternative approaches. Quant. Inf. Process. 14 (2015) 2195.
[30] Zhou N. R., Li J. F., Yu Z. B., Gong L. H. and Farouk A., New quantum dialogue protocol based on continuous-variable two-mode squeezed vacuum states. Quant. Inf. Process. 16 (2017) 4.
[31] Chauhan S. and Gupta N. L., Bidirectional Quantum Secure Direct Communication Using Dense Coding of Four Qubit Cluster States. J. Sci.
Res. 14 (2022) 179.
[32] Nguyen B. A., Quantum dialogue by nonselective measurements. Adv. Nat. Sci. Nanosci. Nanotech. 9 (2018) 025001.
[33] Nguyen B. A., Quantum dialogue mediated by EPR-type entangled coherent states. Quant. Inf. Process. 20 (2021) 100.
[34] Lang Y. F., Efficient Quantum Dialogue Using a Photon in Double Degrees of Freedom. Int. J. Theor. Phys. 61 (2022) 105.
[35] Ramachandran M. and Balakrishnan S., Significance of Bell States Over Four-Qubit Entangled States in Quantum Bidirectional Direct Communication Protocols. Int. J. Theor. Phys. 62 (2023) 180.
[36] Paul G. and Kwiat J., Hyper-entangled states. Mod. Opt. 44 (1997)2173.
[37] Deng F. G., Ren B. C. and Li X. H., Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62 (2017) 46.
[38] Wang X. L., Cai X. D., Su Z. E., Chen M. C., Wu D., Li L., Liu N. L., Lu C. Y. and Pan J. W., Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518 (2015) 516.
[39] Graham T. M., Bernstein H. J., Wei T. C., Junge M. and Kwiat P. G., Superdense teleportation using hyperentangled photons. Nat. Commun. 6 (2015) 7185.
[40] Luo M. X., Li H. R., Lai H. and Wang X., Teleportation of a ququart system using hyperentangled photons assisted by atomic-ensemble memories.
Phys. Rev. A 93 (2016) 012332.
[41] Walborn S. P., Breaking the communication barrier. Nat. Phys. 4 (2008) 268.
[42] Barreiro J. T., Wei T. C. and Kwiat P. G., Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4 (2008)282.
[43] Williams B. P., Sadlier R. J. and Humble T. S., Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements. Phys. Rev. Lett. 118 (2017) 050501. Secure direct message exchange ... 19
[44] Nawaz M., ul-Islam R. and Ikram M., Remote state preparation through hyperentangled atomic state. J. Phys. B: At. Mol. Opt. Phys. 51 (2018) 075501.
[45] Zhou P., Jiao X. F. and Lv S. X., Parallel remote state preparation of arbitrary single-qubit states via linear-optical elements by using hyperentangled Bell states as the quantum channel. Quant. Inf. Process. 17 (2018) 298.
[46] Jiao X. F., Zhou P., Lv S. X. and Wang Z. Y., Remote preparation for single-photon two-qubit hybrid state with hyperentanglement via linearopticalelements. Sci. Rep. 9 (2019) 4663.
[47] Zhou P. and Lv L., Joint remote preparation of single-photon three qubit state with hyperentangled state via linear-optical elements. Quant.Inf. Process. 19 (2020) 283.
[48] Jiao X. F., Zhou P. and Lv S. X., Remote implementation of single qubit operations via hyperentangled states with cross-Kerr nonlinearity. J.Opt. Soc. Am. B 36 (2019) 867.
[49] Nguyen B. A. and Cao T. B., Controlled remote implementation of operators via hyperentanglement. J. Phys. A: Math. Theor. 55 (2022) 225307.
[50] Nguyen B. A., Joint remote implementation of operators. J. Phys. A: Math. Theor. 55 (2022) 395304
[51] Wu X. D., Zhou L., Zhong W. and Sheng Y. B., High-capacity measurement-device-independent quantum secure direct communication. Quant. Inf. Process. 19 (2020) 354.
[52] Gao C. Y., Guo P. L. and Ren B. C., Efficient quantum secure direct communication with complete Bell-state measurement. Quantum Eng. 3 (2021) e83.
[53] Sheng Y. B., Zhou L. and Long G. L., One-step quantum secure direct communication. Sci. Bull. 67 (2022) 367.
[54] Meng Y., Qu Z., Muhammad G. and Tiwari P., Secure and efficient data transmission based on quantum dialogue with hyperentangled states in cloud office. Internet of Things 24 (2023) 100911.
[55] Calsamiglia J. and Lutkenhaus N., Maximum efficiency of a linear-optical Bell-state analyzer. App. Phys. B 72 (2001) 67.
[56] Holevo A. S., Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel. Problems of Information Transmission 9 (1973) 177.
[57] Gao F., Guo F. Z., Wen Q. Y. and Zhu F. C., Revisiting the security of quantum dialogue and bidirectional quantum secure direct communication. Sci. Chin. Ser. G: Phys., Mech. Astr. 51 (2008) 559.
[58] Tan Y. G. and Cai Q. Y., Classical Correlation in Quantum Dialogue. Int. J. Quant. Inf. 6 (2008) 325.
[2] Shor P. W., Algorithms for Quantum Computation: Discrete Logarithms and Factoring. Proc. 35th Annual Symposium on Foundations of ComputerScience. IEEE Comput. Soc. Press. (1994) 124
[3] Bennett C. H. and Brassard G., Quantum Cryptography: Public Key Distribution and Coin Tossing. Proc. IEEE Int. Conf. Computers, Systems, and Signal Processing (Bangalore) (1984) 175.
[4] Ekert A. K., Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67 (1991) 661.
[5] Bennett C. H., Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68 (1992) 3121.
[6] Shannon C., Communication theory of secrecy systems. Bell System Technical Journal 28 (1949) 656.
[7] Bostrom K. and Felbinger T. F., Deterministic Secure Direct Communication Using Entanglement. Phys. Rev. Lett. 89 (2002) 187902.
[8] Beige A., Englerta B. G., Kurtsieferc Ch.and Weinfurter H., Secure communication with a publicly known key. Acta Phys. Pol. A 101 (2002) 357.
[9] Deng F. G., Long G. L. and Liu X. S., Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A 68 (2003) 042317.
[10] Deng F. G. and Long G. L., Secure direct communication with a quantum one-time pad. Phys. Rev. A 69 (2004) 052319.
[11] Li X. H., Zhou P., Liang Y. J., Li C. Y., Zhou H. Y. and Deng F. G., Quantum Secure Direct Communication Network with Two-Step Protocol. Chin. Phys. Lett. 23 (2006) 1080.
[12] Hu J. Y., Yu B., Jing M. Y., Xiao L. T., Jia S. T., Qin G. Q. and Long G. L., Experimental quantum secure direct communication with single photons. Light: Sci. & Appl. 5 (2016) e16144.
[13] Zhang W., Ding D. S., Sheng Y. B., Zhou L., Shi B. S. and Guo G. C., Quantum Secure Direct Communication with Quantum Memory. Phys. Rev. Lett. 118 (2017) 220501.
[14] Zhu F., Zhang W., Sheng Y. B. and Huang Y. D., Experimental long-distance quantum secure direct communication. Sci. Bull. 62 (2017) 1519.
[15] Pan D., Lin Z. S., Wu J. W., Zhang H. R., Sun Z., Ruan D., Yin L. G. and Long G. L., Experimental free-space quantum secure direct communication and its security analysis. Photon. Res. 8 (2020) 1522.
[16] Srikara S., Thapliyal K. and Pathak A., Continuous variable direct secure quantum communication using Gaussian states. Quant. Inf. Process. 19 (2020) 132.
[17] Nayana D. and Goutam P., Cryptanalysis of quantum secure direct communication protocol with mutual authentication based on single photons and Bell states. Europhys. Lett. 138 (2022) 48001. Secure direct message exchange ... 17
[18] Zhang H. R., Sun Z., Qi R. Y., Yin L. G., Long G. L. and Lu J. H., Realization of quantum secure direct communication over 100 km fiber with time-bin and phase quantum states. Light Sci. & Appl. 11 (2022) 83.
[19] Pan D., Song X. T. and Long G. L., Free-space quantum secure direct communication: basics, progress, and outlook. Advanced Devices & Instrunentation 4 (2023) 0004.
[20] Panda S. S., Yasir P. A. A. and Chandrashekar C. M., Quantum direct communication protocol using recurrence in k-cycle quantum walks. Phys. Rev. A 107 (2023) 022611.
[21] Nguyen B. A., Quantum dialogue. Phys. Lett. A 328 (2004) 6.
[22] Nguyen B. A., Secure dialogue without a prior key distribution. J. Kor. Phys. Soc. 47 (2005) 562.
[23] Yan C., Man Z. X. and Xia Y. J., Quantum Bidirectional Secure Direct Communication via Entanglement Swapping. Chin. Phys. Lett. 24(2007) 19.
[24] Shi G. F., Xi X. Q. and Tian X. L., Bidirectional quantum securecommunication based on a shared private Bell state. Opt. Commun. 282(2009) 2460.
[25] Shan C. J., Liu J. B., Cheng W. W., Liu T. K., Huang Y. X. and Li H., Bidirectional quantum secure direct communication in drivencavity QED. Mod. Phys. Lett. B 23 (2009) 3225.
[26] Shi G. F., Xi X. Q. and Hu M. L., Quantum secure dialogue by usingsingle photons. Opt. Commun. 283 (2010) 1984.
[27] Gao G., Two quantum dialogue protocols without information leakage. Opt. Commun. 283 (2010) 2288.
[28] Shi G. F., Bidirectional quantum secure communication scheme based on Bell states and auxiliary particles. Opt. Commun. 283 (2010) 5275.
[29] Pathak A., Efficient protocols for unidirectional and bidirectional controlled deterministic secure quantum communication: different alternative approaches. Quant. Inf. Process. 14 (2015) 2195.
[30] Zhou N. R., Li J. F., Yu Z. B., Gong L. H. and Farouk A., New quantum dialogue protocol based on continuous-variable two-mode squeezed vacuum states. Quant. Inf. Process. 16 (2017) 4.
[31] Chauhan S. and Gupta N. L., Bidirectional Quantum Secure Direct Communication Using Dense Coding of Four Qubit Cluster States. J. Sci.
Res. 14 (2022) 179.
[32] Nguyen B. A., Quantum dialogue by nonselective measurements. Adv. Nat. Sci. Nanosci. Nanotech. 9 (2018) 025001.
[33] Nguyen B. A., Quantum dialogue mediated by EPR-type entangled coherent states. Quant. Inf. Process. 20 (2021) 100.
[34] Lang Y. F., Efficient Quantum Dialogue Using a Photon in Double Degrees of Freedom. Int. J. Theor. Phys. 61 (2022) 105.
[35] Ramachandran M. and Balakrishnan S., Significance of Bell States Over Four-Qubit Entangled States in Quantum Bidirectional Direct Communication Protocols. Int. J. Theor. Phys. 62 (2023) 180.
[36] Paul G. and Kwiat J., Hyper-entangled states. Mod. Opt. 44 (1997)2173.
[37] Deng F. G., Ren B. C. and Li X. H., Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62 (2017) 46.
[38] Wang X. L., Cai X. D., Su Z. E., Chen M. C., Wu D., Li L., Liu N. L., Lu C. Y. and Pan J. W., Quantum teleportation of multiple degrees of freedom of a single photon. Nature 518 (2015) 516.
[39] Graham T. M., Bernstein H. J., Wei T. C., Junge M. and Kwiat P. G., Superdense teleportation using hyperentangled photons. Nat. Commun. 6 (2015) 7185.
[40] Luo M. X., Li H. R., Lai H. and Wang X., Teleportation of a ququart system using hyperentangled photons assisted by atomic-ensemble memories.
Phys. Rev. A 93 (2016) 012332.
[41] Walborn S. P., Breaking the communication barrier. Nat. Phys. 4 (2008) 268.
[42] Barreiro J. T., Wei T. C. and Kwiat P. G., Beating the channel capacity limit for linear photonic superdense coding. Nat. Phys. 4 (2008)282.
[43] Williams B. P., Sadlier R. J. and Humble T. S., Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements. Phys. Rev. Lett. 118 (2017) 050501. Secure direct message exchange ... 19
[44] Nawaz M., ul-Islam R. and Ikram M., Remote state preparation through hyperentangled atomic state. J. Phys. B: At. Mol. Opt. Phys. 51 (2018) 075501.
[45] Zhou P., Jiao X. F. and Lv S. X., Parallel remote state preparation of arbitrary single-qubit states via linear-optical elements by using hyperentangled Bell states as the quantum channel. Quant. Inf. Process. 17 (2018) 298.
[46] Jiao X. F., Zhou P., Lv S. X. and Wang Z. Y., Remote preparation for single-photon two-qubit hybrid state with hyperentanglement via linearopticalelements. Sci. Rep. 9 (2019) 4663.
[47] Zhou P. and Lv L., Joint remote preparation of single-photon three qubit state with hyperentangled state via linear-optical elements. Quant.Inf. Process. 19 (2020) 283.
[48] Jiao X. F., Zhou P. and Lv S. X., Remote implementation of single qubit operations via hyperentangled states with cross-Kerr nonlinearity. J.Opt. Soc. Am. B 36 (2019) 867.
[49] Nguyen B. A. and Cao T. B., Controlled remote implementation of operators via hyperentanglement. J. Phys. A: Math. Theor. 55 (2022) 225307.
[50] Nguyen B. A., Joint remote implementation of operators. J. Phys. A: Math. Theor. 55 (2022) 395304
[51] Wu X. D., Zhou L., Zhong W. and Sheng Y. B., High-capacity measurement-device-independent quantum secure direct communication. Quant. Inf. Process. 19 (2020) 354.
[52] Gao C. Y., Guo P. L. and Ren B. C., Efficient quantum secure direct communication with complete Bell-state measurement. Quantum Eng. 3 (2021) e83.
[53] Sheng Y. B., Zhou L. and Long G. L., One-step quantum secure direct communication. Sci. Bull. 67 (2022) 367.
[54] Meng Y., Qu Z., Muhammad G. and Tiwari P., Secure and efficient data transmission based on quantum dialogue with hyperentangled states in cloud office. Internet of Things 24 (2023) 100911.
[55] Calsamiglia J. and Lutkenhaus N., Maximum efficiency of a linear-optical Bell-state analyzer. App. Phys. B 72 (2001) 67.
[56] Holevo A. S., Bounds for the Quantity of Information Transmitted by a Quantum Communication Channel. Problems of Information Transmission 9 (1973) 177.
[57] Gao F., Guo F. Z., Wen Q. Y. and Zhu F. C., Revisiting the security of quantum dialogue and bidirectional quantum secure direct communication. Sci. Chin. Ser. G: Phys., Mech. Astr. 51 (2008) 559.
[58] Tan Y. G. and Cai Q. Y., Classical Correlation in Quantum Dialogue. Int. J. Quant. Inf. 6 (2008) 325.