Abstract
In this paper, the first high-capacity quantum private comparison (QPC) protocol is proposed to solve the comparison problem of equality of two parties’ secret inputs without revealing them out. This scheme is assisted with the semi-honest third party to fulfill the task. And the genuine two-photon hyperentangled Bell states are utilized as the important information carriers. Different from the previous protocols, this hyperentangled Bell states are composed of only two photons but characterize six qubits in two longitudinal momentum and polarization degrees of freedom (DOFs). In addition, this protocol possesses a higher information capacity and saves massive quantum resources for that the two-photon system can carry 6 bits of information. Meanwhile, this scheme can be applied and useful for long-distance quantum communication to improve the feasibility of QPC protocol. Furthermore, 64 nonorthogonal single-photon states as decoy photons are utilized to detect the security of the quantum channel. This method not only increases the security of the quantum channel, but also decreases the decoherence effect of environment noise. Moreover, this QPC protocol is analyzed to be immune to various kinds of attack. Finally, this QPC protocol can obtain the good application to compare the secret inputs securely, efficiently and feasibly.
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C.H. Bennett, G. Brassard, Quantum cryptography: public key distribution and coin tossing, in Proceedings of IEEE International Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Bangalore, Vol. 175
A.-K. Ekert, Phys. Rev. Lett. 67, 661 (1991)
C.-H. Bennett, G. Brassard, N.-D. Mermin, Phys. Rev. Lett. 68, 557 (1992)
C. Zhang, J. Zhu, Q. Wang, Eur. Phys. J. D 72, 108 (2018)
Y.-Y. Fei, X.-D. Meng, M. Gao, Z. Ma, H. Wang, Eur. Phys. J. D 72, 107 (2018)
J. Zhu, C. Zhang, Q. Wang, Eur. Phys. J. D 71, 319 (2017)
H. Jiang, M. Gao, B. Yan, W. Wang, Z. Ma, Eur. Phys. J. D 70, 78 (2016)
F. Gao, S.-J. Qin, F.-Z. Guo, Q.-Y. Wen, IEEE J. Quantum Electron. 47, 630 (2011)
F. Gao, F.-Z. Guo, Q.-Y. Wen, F.-C. Zhu, Int. J. Mod. Phys. B 24, 4611 (2010)
F. Gao, F.-Z. Guo, Q.-Y. Wen, F.-C. Zhu, Phys. Lett. A 355, 172 (2006)
B. Liu, F. Gao, Q.-Y. Wen, IEEE J. Quantum Electron. 47, 1383 (2011)
J. Wang, H. Wang, X. Qin, Z. Wei, Z. Zhang, Eur. Phys. J. D 70, 5 (2016)
Y.-G. Tan, Q.-Y. Cai, H.-F. Yang, Y.-H. Hu, Eur. Phys. J. D 69, 258 (2015)
J.-Z. Huang, Z.-Q. Yin, S. Wang, H.-W. Li, W. Chen, Z.-F. Han, Eur. Phys. J. D 66, 159 (2012)
M. Hillery, V. Bužek, A. Berthiaume, Phys. Rev. A 59, 1829 (1999)
A. Karlsson, M. Koashi, N. Imoto, Phys. Rev. A 59, 162 (1999)
C.-M. Bai, Z.-H. Li, M.-M. Si, Y.-M. Li, Eur. Phys. J. D 71, 255 (2017)
H.-Y. Jia, Q.-Y. Wen, F. Gao, S.-J. Qin, F.-Z. Guo, Phys. Lett. A 376, 1035 (2012)
F. Gao, F.-Z. Guo, Q.-Y. Wen, F.-C. Zhu, Phys. Rev. A 72, 036302 (2005)
F.-G. Deng, X.-H. Li, C.-Y. Li, P. Zhou, H.-Y. Zhou, Phys. Rev. A 72, 044301 (2005)
F.-G. Deng, H.-Y. Zhou, G.-L. Long, Phys. Rev. A 337, 329 (2005)
M. Ray, S. Chatterjee, I. Chakrabarty, Eur. Phys. J. D 70, 114 (2016)
Z.-J. Zhang, J. Yang, Z.-X. Man, Y. Li, Eur. Phys. J. D 33, 133 (2005)
G.-L. Long, X.-S. Liu, Phys. Rev. A 65, 032302 (2002)
F.-G. Deng, G.-L. Long, X.-S. Liu, Phys. Rev. A 68, 042317 (2003)
F.-G. Deng, G.-L. Long, Phys. Rev. A 69, 052319 (2004)
J.-Y. Hu, B. Yu, M.-Y. Jing, L.-T. Xiao, S.-T. Jia, G.-Q. Qin, G.-L. Long, Light Sci. Appl. 5, e16144 (2016)
W. Zhang, D.-S. Ding, Y.-B. Sheng, L. Zhou, B.-S. Shi, G.-C. Guo, Phys. Rev. Lett. 118, 220501 (2017)
C. Wang, F.-G. Deng, Y.-S. Li, X.-S. Liu, G.-L. Long, Phys. Rev. A 71, 044305 (2005)
C. Wang, F.-G. Deng, G.-L. Long, Opt. Commun. 253, 15 (2005)
X.-H. Li, C.-Y. Li, F.-G. Deng, P. Zhou, Y.-J. Liang, H.-Y. Zhou, Chin. Phys. 16, 2149 (2007)
G.-L. Long, F.-G. Deng, C. Wang, X.-H. Li, K. Wen, W.-Y. Wang, Front. Phys. China 2, 251 (2007)
B.-C. Ren, H.-R. Wei, M. Hua, T. Li, F.-G. Deng, Eur. Phys. J. D 67, 30 (2013)
T.-J. Wang, T. Li, F.-F. Du, F.-G. Deng, Chin. Phys. Lett. 28, 040305 (2011)
F. Gao, Q.-Y. Wen, F.-C. Zhu, Chin. Phys. B 17, 3189 (2008)
F. Gao, S.-J. Qin, F.-Z. Guo, Q.-Y. Wen, Chin. Phys. Lett. 28, 020303 (2011)
F. Gao, S.-J. Qin, Q.-Y. Wen, F.-C. Zhu, Opt. Commun. 283, 192 (2010)
B. Liu, F. Gao, W. Huang, Q.Y. Wen, Quantum Inf. Process. 12, 1797 (2013)
W. Huang, Q.-Y. Wen, B. Liu, F. Gao, Quantum Inf. Process. 13, 649 (2014)
Y.-H. Chou, G.-J. Zeng, Z.-H. Chang, S.-Y. Kuo, Sci. Rep. 8, 4633 (2018)
F. Gao, B. Liu, W. Huang, Q.-Y. Wen, IEEE J. Sel. Top. Quant. 21, 98 (2015)
B. Liu, F. Gao, W. Huang, Q.Y. Wen, Sci. China Phys. Mech. Astron. 58, 100301 (2015)
C.-Y. Wei, T.-Y. Wang, F. Gao, Phys. Rev. A 93, 042318 (2016)
C.-Y. Wei, F. Gao, Q.-Y. Wen, T.-Y. Wang, Sci. Rep. 4, 7537 (2014)
C.-Y. Wei, X.-Q. Cai, B. Liu, T.-Y. Wang, F. Gao, IEEE Trans. Comput. 67, 2 (2018)
A.C. Yao, Protocols for secure computations, in Proceedings of the 23rd Annual Symposium on Computer Science, Chicago, 1982, p. 160
Y.-G. Yang, Q.-Y. Wen, J. Phys. A Math. Theor. 42, 055305 (2009)
H.-Y. Tseng, J. Lin, T. Hwang, Quantum Inf. Process. 11, 373 (2012)
W. Liu, Y.-B. Wang, Z.-T. Jiang, Opt. Commun. 284, 3160 (2011)
W. Huang, Q.-Y. Wen, B. Liu, F. Gao, Y. Sun, Sci. China Phys. Mech. Astron. 56, 1670 (2013)
Z.-W. Sun, D.-Y. Long, Int. J. Theor. Phys. 52, 212 (2013)
J. Li, H.-F. Zhou, L. Jia, T.-T. Zhang, Int. J. Theor. Phys. 53, 2167 (2014)
Y. Chang, W.-B. Zhang, S.-B. Zhang, H.-C. Wang, L.-L. Yan, G.-H. Han, Z.-W. Sheng, Y.-Y. Huang, W. Suo, J.-X. Xiong, Commun. Theor. Phys. 66, 621 (2016)
T.-Y. Ye, Commun. Theor. Phys. 67, 147 (2017)
O. Pfister, Nat. Photonics 9, 483 (2015)
F.-G. Deng, B.-C. Ren, X.-H. Li, Sci. Bull. 62, 46 (2017)
Y.-B. Sheng, F.-G. Deng, G.-L. Long, Phys. Rev. A 82, 032318 (2010)
B.-C. Ren, H.-R. Wei, M. Hua, T. Li, F.-G. Deng, Opt. Express 20, 24664 (2012)
T.-J. Wang, Y. Lu, G.-L. Long, Phys. Rev. A 86, 042337 (2012)
X.-H. Li, S. Ghose, Phys. Rev. A 93, 022302 (2016)
G.-Y. Wang, Q. Ai, B.-C. Ren, T. Li, F.-G. Deng, Opt. Express 24, 28444 (2016)
Q. Liu, G.-Y. Wang, Q. Ai, M. Zhang, F.-G. Deng, Sci. Rep. 6, 22016 (2016)
P. Wang, W. Fan, M. Chen, O. Pfister, N.-C. Menicucci, Engineering large-scale entanglement in the quantum optical frequency comb, in 2015 IEEE Conference on In Lasers and Electro-Optics (CLEO), San Jose, 2015, p. 1
B.-C. Ren, H.-R. Wei, F.-G. Deng, Laser Phys. Lett. 10, 095202 (2013)
B.-C. Ren, F.-G. Deng, Sci. Rep. 4, 4623 (2014)
B.-C. Ren, G.-Y. Wang, F.-G. Deng, Phys. Rev. A 91, 032328 (2015)
T. Li, G.-L. Long, Phys. Rev. A 94, 022343 (2016)
B.-C. Ren, F.-G. Deng, Opt. Express 25, 10863 (2017)
H.-R. Wei, F.-G. Deng, G.-L. Long, Opt. Express 24, 18619 (2016)
T.-J. Wang, Y. Zhang, C. Wang, Laser Phys. Lett. 11, 025203 (2014)
R.-N. Alexander, P. Wang, N. Sridhar, M. Chen, O. Pfister, N.-C. Menicucci, Phys. Rev. A 94, 032327 (2016)
W. Fan, P. Wang, O. Pfister, Broadband quasiphasematching for large-scale entanglement in quantum optical frequency combs, in CLEO: 2014, OSA Technical Digest (Optical Society of America, Washington, DC, 2014) paper JW2A.126
M. Chen, N.-C. Menicucci, O. Pfister, Phys. Rev. Lett. 112, 120505 (2014)
M. Pysher, Y. Miwa, R. Shahrokhshahi, R. Bloomer, O. Pfister, Phys. Rev. Lett. 107, 030505 (2011)
Y.-B. Sheng, F.-G. Deng, Phys. Rev. A 81, 032307 (2010)
Y.-B. Sheng, F.-G. Deng, Phys. Rev. A 82, 044305 (2010)
Y.-B. Sheng, L. Zhou, Sci. Rep. 5, 7815 (2015)
F.-G. Deng, Phys. Rev. A 83, 062316 (2011)
T.-J. Wang, S.-Y. Song, G.-L. Long, Phys. Rev. A 85, 062311 (2012)
B.-C. Ren, F.-F. Du, F.-G. Deng, Phys. Rev. A 88, 012302 (2013)
B.-C. Ren, G.-L. Long, Opt. Express 22, 6547 (2014)
X. Li, S. Ghose, Laser Phys. Lett. 11, 125201 (2014)
B.-C. Ren, G.-L. Long, Sci. Rep. 5, 16444 (2015)
H.-J. Liu, Y. Xia, J. Song, Quantum Inf. Process. 15, 2033 (2016)
L. Zhou, Y.-B. Sheng, Opt. Commun. 313, 217 (2014)
Y.-B. Sheng, L. Zhou, L. Wang, S.-M. Zhao, Quantum Inf. Process. 12, 1885 (2013)
Y.-B. Sheng, L. Zhou, Entropy 15, 1776 (2013)
Y.-B. Sheng, L. Zhou, J. Opt. Soc. Am. B 30, 678 (2013)
B.-C. Ren, F.-F. Du, F.-G. Deng, Phys. Rev. A 90, 052309 (2014)
F.-F. Du, T. Li, G.-L. Long, Ann. Phys. 375, 105 (2016)
Y.-B. Sheng, L. Zhou, G.L. Long, Phys. Rev. A 88, 022302 (2013)
D. Patrick, T. Calarco, S. Montangero, Phys. Rev. Lett. 106, 190501 (2011)
D. Burgarth, K. Maruyama, M. Murphy, S. Montangero, T. Calarco, F. Nori, M.-B. Plenio, Phys. Rev. A 81, 040303 (2010)
S. Hoyer, F. Caruso, S. Montangero, M. Sarovar, T. Calarco, M.-B. Plenio, K.-B. Whaley, New J. Phys. 16, 045007 (2014)
V. Siddhu, Quantum Inf. Process. 14, 3005 (2015)
R. Ceccarelli, G. Vallone, F.-D. Martini, P. Mataloni, A. Cabello, Phys. Rev. Lett. 103, 160401 (2009)
C.-Y. Li, H.-Y. Zhou, Y. Wang, F.-G. Deng, Chin. Phys. Lett. 22, 1049 (2005)
F. Gao, S.-J. Qin, Q.-Y. Wen, F.-C. Zhu, Quantum Inf. Comput. 7, 329 (2007)
T. Chaneliere, D.-N. Matsukevich, S.-D. Jenkins, S.-Y. Lan, T.-A.B. Kennedy, A. Kuzmich, Nature 438, 833 (2005)
A.-I. Lvovsky, B.-C. Sanders, W. Tittel, Nat. Photonics 3, 706 (2009)
D.-S. Ding, Raman quantum memory of photonic polarized entanglement, in Broad Bandwidth and High Dimensional Quantum Memory Based on Atomic Ensembles (Springer, Singapore, 2018), p. 91
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Contribution to the Topical Issue “Quantum Correlations”, edited by Marco Genovese, Vahid Karimipour, Sergei Kulik, and Olivier Pfister.
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Xu, L., Zhao, Zw. High-capacity quantum private comparison protocol with two-photon hyperentangled Bell states in multiple-degree of freedom. Eur. Phys. J. D 73, 58 (2019). https://doi.org/10.1140/epjd/e2019-90374-y
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DOI: https://doi.org/10.1140/epjd/e2019-90374-y