Abstract
At first, the entanglement source deployment problem is studied in a quantum multi-hop network, which has a significant influence on quantum connectivity. Two optimization algorithms are introduced with limited entanglement sources in this paper. A deployment algorithm based on node position (DNP) improves connectivity by guaranteeing that all overlapping areas of the distribution ranges of the entanglement sources contain nodes. In addition, a deployment algorithm based on an improved genetic algorithm (DIGA) is implemented by dividing the region into grids. From the simulation results, DNP and DIGA improve quantum connectivity by 213.73% and 248.83% compared to random deployment, respectively, and the latter performs better in terms of connectivity. However, DNP is more flexible and adaptive to change, as it stops running when all nodes are covered.
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References
H. J. Kimble, The quantum internet, Nature 453(7198), 1023 (2008)
C. H. Bennett, G. Brassard, C. Crepeau, 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(13), 1895 (1993)
D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature 390(6660), 575 (1997)
A. Karlsson and M. Bourennane, Quantum teleportation using three-particle entanglement, Phys. Rev. A 58(6), 4394 (1998)
F. L. Yan and T. Yan, Probabilistic teleportation via a nonmaximally entangled GHZ state, Chin. Sci. Bull. 55(10), 902 (2010)
A. K. Pati, Assisted cloning and orthogonal complementing of an unknown state, Phys. Rev. A 61, 022308 (1999)
P. Espoukeh and P. Pedram, Quantum teleportation through noisy channels with multi-qubit GHZ states, Quantum Inform. Process. 13(8), 1789 (2014)
P. Agrawal and A. Pati, Perfect teleportation and superdense coding with W states, Phys. Rev. A 74(6), 062320 (2006)
S. Adhikari, A. S. Majumdar, S. Roy, B. Ghosh, and N. Nayak, Teleportation via maximally and non-maximally entangled mixed states, Quantum Inf. Comput. 10(5–6), 0398 (2010)
F. Verstraete and H. Verschelde, Optimal teleportation with a mixed state of two qubits, Phys. Rev. Lett. 90(9), 097901 (2003)
G. Rigolin, Quantum teleportation of an arbitrary two qubit state and its relation to multipartite entanglement, Phys. Rev. A 71, 032303 (2005)
S. Muralidharan and P. K. Panigrahi, Perfect teleportation, quantum state sharing and superdense coding through a genuinely entangled five-qubit state, Phys. Rev. A 77(3), 032321 (2008)
D. P. Tian, Y. J. Tao, and M. Qin, Teleportation of an arbitrary two-qudit state based on the non-maximally four qudit cluster state, Sci. China G 51, 1523 (2008)
J. C. Liu, Y. H. Li, and Y. Y. Nie, Controlled teleportation of an arbitrary two-particle pure or mixed state by using a five-qubit cluster state, Int. J. Theor. Phys. 49(8), 1976 (2010)
Y. L. Liu, Z. X. Man, and Y. J. Xia, Quantum teleportation of an arbitrary n-qubit state via non-maximally entangled state, Int. J. Quant. Inf. 5(05), 673 (2007)
D. Saha and P. K. Panigrahi,N-qubit quantum teleportation, information splitting and superdense coding through the composite GHZ-Bell channel, Quantum Inform. Process. 11(2), 615 (2012)
P. X. Chen, S. Y. Zhu, and G. C. Guo, General form of genuine multipartite entanglement quantum channels for teleportation, Phys. Rev. A 74(3), 032324 (2006)
A. K. Ekert, Quantum cryptography based on Bell theorem, Phys. Rev. Lett. 67(6), 661 (1991)
R. Ursin, F. Tiefenbacher, T. Schmitt-Manderbach, H. Weier, T. Scheidl, M. Lindenthal, B. Blauensteiner, T. Jennewein, J. Perdigues, P. Trojek, B. Ömer, M. Fürst, M. Meyenburg, J. Rarity, Z. Sodnik, C. Barbieri, H. Weinfurter, and A. Zeilinger, Entanglement-based quantum communication over 144 km, Nat. Phys. 3(7), 481 (2007)
F. G. Deng, G. L. Long, and X. S. Liu, A Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block, Phys. Rev. A 68(4), 042317 (2003)
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(9), e16144 (2016)
M. Cao, S. Q. Zhu, and J. X. Fang, Teleportation of n-particle state via n pairs of EPR channels, Commum. Theor. Phys. 41(5), 689 (2004)
P. R. Tapster, J. G. Rarity, and P. C. M. Owens, Violation of Bell’s inequality over 4 km of optical fiber, Phys. Rev. Lett. 73(14), 1923 (1994)
W. Tittel, J. Brendel, H. Zbinden, and N. Gisin, Violation of Bell inequalities by photons more than 10 km apart, Phys. Rev. Lett. 81(17), 3563 (1998)
H. J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81(26), 5932 (1998)
M. Aspelmeyer, H. R. Böhm, T. Gyatso, T. Jennewein, R. Kaltenbaek, M. Lindenthal, G. Molina-Terriza, A. Poppe, K. Resch, M. Taraba, R. Ursin, P. Walther, and A. Zeilinger, Long-distance free-space distribution of quantum entanglement, Science 301(5633), 621 (2003)
C. Z. Peng, T. Yang, X. H. Bao, J. Zhang, X. M. Jin, F. Y. Feng, B. Yang, J. Yang, J. Yin, Q. Zhang, N. Li, B. L. Tian, and J. W. Pan, Experimental free-space distribution of entangled photon pairs over 13 km: Towards satellite-based global quantum communication, Phys. Rev. Lett. 94(15), 150501 (2005)
A. Fedrizzi, R. Ursin, T. Herbst, M. Nespoli, R. Prevedel, T. Scheidl, F. Tiefenbacher, T. Jennewein, and A. Zeilinger, High-fidelity transmission of entanglement over a high-loss freespace channel, Nat. Phys. 5(6), 389 (2009)
D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein–Podolsky–Rosen channels, Phys. Rev. Lett. 80(6), 1121 (1998)
X. M. Jin, J. G. Ren, B. Yang, Z. H. Yi, F. Zhou, X. F. Xu, S. K. Wang, D. Yang, Y. F. Hu, S. Jiang, T. Yang, H. Yin, K. Chen, C. Z. Peng, and J. W. Pan, Experimental free-space quantum teleportation, Nat. Photonics 4(6), 376 (2010)
J. Yin, J. G. Ren, H. Lu, Y. Cao, H. L. Yong, Y. P. Wu, C. Liu, S. K. Liao, F. Zhou, Y. Jiang, X. D. Cai, P. Xu, G. S. Pan, J. J. Jia, Y. M. Huang, H. Yin, J. Y. Wang, Y. A. Chen, C. Z. Peng, and J. W. Pan, Quantum teleportation and entanglement distribution over 100-kilometre free-space channels, Nature 488(7410), 185 (2012)
X. T. Yu, Z. C. Zhang, and J. Xu, Distributed wireless quantum communication networks with partially entangled pairs, Chin. Phys. B 23, 010303 (2014)
L. H. Shi, X. T. Yu, X. F. Cai, Y. X. Gong, and Z. C. Zhang, Quantum information transmission in the quantum wireless multihop network based on Werner state, Chin. Phys. B 24(5), 050308 (2015)
X. F. Cai, X. T. Yu, L. H. Shi, and Z. C. Zhang, Partially entangled states bridge in quantum teleportation, Front. Phys. 9(5), 646 (2014)
K. Wang, X. T. Yu, S. L. Lu, and Y. X. Gong, Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation, Phys. Rev. A 89, 022329 (2014)
P. Y. Xiong, X. T. Yu, H. T. Zhan, and Z. C. Zhang, Multiple teleportation via partially entangled GHZ state, Front. Phys. 11(4), 110303 (2016)
Z. Z. Zou, X. T. Yu, Y. X. Gong, and Z. C. Zhang, Multihop teleportation of two-qubit state via the composite GHZ-Bell channel, Phys. Lett. A 381(2), 76 (2017)
N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Quantum cryptography, Rev. Mod. Phys. 74(1), 145 (2002)
C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels, Phys. Rev. Lett. 76(5), 722 (1996)
J. W. Pan, C. Simon, Č Brukner, and A. Zeilinger, Entanglement purification for quantum communication, Nature 410(6832), 1067 (2001)
F. G. Deng, One-step error correction for multipartite polarization entanglement, Phys. Rev. A 83(6), 062316 (2011)
Y. B. Sheng, J. Pan, R. Guo, L. Zhou, and L. Wang, Efficient N-particle W state concentration with different parity check gates, Sci. China Phys. Mech. Astron. 58(6), 1 (2015)
L. Zhou and Y. B. Sheng, Purification of logic-qubit entanglement, Sci. Rep. 6(1), 28813 (2016)
G. Boudreau, J. Panicker, N. Guo, R. Chang, N. Wang, and S. Vrzic, Interference coordination and cancellation for 4G networks, IEEE Commun. Mag. 47(4), 74 (2009)
E. Q. V. Martins and M. M. B. Pascoal, A new implementation of Yen’s ranking loopless paths algorithm, Quarterly Journal of the Belgian, French and Italian Operations Research Societies, 1(2), 121 (2003)
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This project was supported by the National Natural Science Foundation of China (Grant Nos. 61571105 and 61601120).
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Zou, ZZ., Yu, XT. & Zhang, ZC. Quantum connectivity optimization algorithms for entanglement source deployment in a quantum multi-hop network. Front. Phys. 13, 130202 (2018). https://doi.org/10.1007/s11467-017-0721-7
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DOI: https://doi.org/10.1007/s11467-017-0721-7