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The optimal relay path calculation and selection are important factors to affect the performance of quantum communication network. Current researches seldom consider the quantum path selection in real noisy environments. One of the difficult problems is how to analyze the influence of the noise on the quantum communication in multi-hop channels. This paper aims to solve the path selection problem of the quantum teleportation network in noisy environments. The process of entanglement swapping in the phase damping channel is first studied with an example of two-hop quantum channel, whose damping factors are p1 and p2. The entanglement states |φ> 12+ and |φ> 34+ are distributed separately in each hop. After the entanglement swapping, the density matrix of the entanglement state of photon 1 and photon 4 is obtained by performing a partial trace over the environment. Then, the Bures fidelity of this entanglement is calculated. After that, we define the path equivalent damping factor to describe the characteristic of the two-hop noisy quantum relay path. With an equivalent calculation method, the results above can be generalized to multi-hop channel. The path equivalent damping factor of the multi-hop amplitude damping channel is also obtained. According to these results, we propose an optimal relay protocol for the quantum teleportation network with the criterion of path equivalent damping factor, which means that a relay path with the minimum path equivalent damping factor can obtain the highest teleportation fidelity. The types and parameters of the messages used in the protocol are given. The processes of the relay protocol are described specifically, including neighbor finding, quantum link noise measurement, and quantum link status transmission. An improved Dijkstra algorithm is used in the optimal path calculation. Furthermore, because the entanglement resources maintained in the quantum nodes are limited and may be exhausted in superior quantum links, we propose a resource reservation method to avoid the failure of the relay path setup. Theoretical analysis and simulation show that our method can obtain a lower average equivalent damping factor and higher teleportation fidelity. It can also be seen that increasing the number of the entanglement resources will raise the performance of the quantum network, however, it brings higher cost and complexity. Therefore, the entanglement resources maintained in the quantum nodes must be configured reasonably according to the network scale, the cost, the time delay and the need of the users.
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Keywords:
- quantum network /
- entanglement swapping /
- quantum noise /
- path selection
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[21] Cheng S T, Wang C Y, Tao M H 2005 IEEE J. Sel. Areas Commun. 23 1424
[22] Yu X T, Zhang Z C, Xu J 2014 Chin. Phys. B 23 010303
[23] Ma H Y, Guo Z W, Fan X K, Wang S M 2015 Acta Electron. Sin. 43 171 (in Chinese) [马鸿洋, 郭忠文, 范兴奎, 王淑梅 2015 电子学报 43 171]
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[25] Zhang Y D 2012 Principles of Quantum Information Physics (Beijing: Science Press) pp147-253 (in Chinese) [张永德 2012 量子信息物理原理(北京: 科学出版社) 第147–172页]
[26] Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722
[27] Nicolas S, Christoph S, Hugues D R, Nicolas G 2011 Rev. Mod. Phys. 83 33
[28] Fujiwara A 2004 Phys. Rev. A 70 012317
[29] Sarovar M, Milburn G J 2006 J. Phys. A: Math. Gen. 39 8487
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[1] Sergienko A V 2006 Quantum Communications and Cryptography (Florida: Taylor & Francis Group CRC Press) pp83-102
[2] Poppe A, Peev M, Maurhart O 2008 Int. J. Quantum Inf. 6 209
[3] Xu F X, Chen W, Wang S, Yin Z Q, Zhang Y, Liu Y, Zhou Z, Zhao Y B, Li H W, Liu D, Han Z F, Guo G C 2009 Chin. Sci. Bull. 54 2991
[4] Xu H X 2014 J. CAEIT 9 259 (in Chinese) [许华醒 2014 中国电子科学研究院学报 9 259]
[5] Hughes R J, Buttler W T, Kwiat P G, Lamoreuax S K, Morgan G L, Nordholt J E, Peterson C G 2000 Aerospace Conference Proceedings, 2000 IEEE Big Sky MT, USA, March 18-25, 2000 p191
[6] Ursin R, Jennewein T, Kofler J, Perdigues J M, Cacciapuoti L, Zeilinger A 2009 Europhys. News 40 26
[7] Toyoshima M, Takayama Y, Takahashi T, Suzuki K, Kimura S 2008 IEEE Aerosp. Electron. Syst. Mag. 23 10
[8] Yin J, Cao Y, Liu S B, Pan G S, Wang J H, Yang T, Pan J W 2013 Opt. Express 21 20032
[9] Heilmann R, Gräfe M, Nolte S, Szameit A 2015 Sci. Bull. 60 96
[10] Su X L, Jia X J, Xie C D, Peng K C 2014 Sci. China: Phys. Mech. Astron. 57 1210
[11] Wang W Y, Wang C, Zhang G Y 2009 Chin. Sci. Bull. 54 158
[12] Wang C Z, Guo H, Ren J G, CaoY, Peng C Z, Liu W Y 2014 Sci. China: Phys. Mech. Astron. 57 1233
[13] Long G L, Li Y S, Zhang W L, Niu L 1999 Phys. Lett. A 262 27
[14] Botsinis P, Ng S X, Hanzo L 2013 Access. IEEE 1 94
[15] Wang J, Chen H Q, Zhang Q, Tang C J 2007 Acta Phys. Sin. 56 673 (in Chinese) [王剑, 陈皇卿, 张权, 唐朝京 2007 56 673]
[16] Wang T Y, Qin S J, Wen Q Y, Zhu F C 2008 Acta Phys. Sin. 57 7452 (in Chinese) [王天银, 秦素娟, 温巧燕, 朱甫臣 2008 57 7452]
[17] Zou X F, Qiu D W 2014 Sci. China: Phys. Mech. Astron. 57 1696
[18] Ma H Y, Qin G Q, Fan X K, Chu P C 2015 Acta Phys. Sin. 64 160306 (in Chinese) [马鸿洋, 秦国卿, 范兴奎, 初鹏程 2015 64 160306]
[19] Nie M, Lu G Y 2008 J. Northwest Univ. (Nat. Sci. Ed.) 38 905 (in Chinese) [聂敏, 卢光跃 2008 西北大学学报自然科学版 38 905]
[20] Liu X H, Pei C X, Nie M 2014 J. Jilin Univ. (Technol. Ed.) 44 1177 (in Chinese) [刘晓慧, 裴昌幸, 聂敏 2014 吉林大学学报工学版 44 1177]
[21] Cheng S T, Wang C Y, Tao M H 2005 IEEE J. Sel. Areas Commun. 23 1424
[22] Yu X T, Zhang Z C, Xu J 2014 Chin. Phys. B 23 010303
[23] Ma H Y, Guo Z W, Fan X K, Wang S M 2015 Acta Electron. Sin. 43 171 (in Chinese) [马鸿洋, 郭忠文, 范兴奎, 王淑梅 2015 电子学报 43 171]
[24] Yin H, Han Y 2012 Quantum Communication Theory and Technology (Beijing: Publishing House of Electronics Industry) pp202-211 (in Chinese) [尹浩, 韩阳 2013 量子通信原理与技术(北京:电子工业出版社)第202–211页]
[25] Zhang Y D 2012 Principles of Quantum Information Physics (Beijing: Science Press) pp147-253 (in Chinese) [张永德 2012 量子信息物理原理(北京: 科学出版社) 第147–172页]
[26] Bennett C H, Brassard G, Popescu S, Schumacher B, Smolin J A, Wootters W K 1996 Phys. Rev. Lett. 76 722
[27] Nicolas S, Christoph S, Hugues D R, Nicolas G 2011 Rev. Mod. Phys. 83 33
[28] Fujiwara A 2004 Phys. Rev. A 70 012317
[29] Sarovar M, Milburn G J 2006 J. Phys. A: Math. Gen. 39 8487
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