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研究了量子态在一条均匀耦合的反铁磁自旋链中传输时, 信道中自旋激发数变化对其传输性质的影响. 利用信息流方法分析输出端粒子的算符演化动力学, 获得了量子态传输的平均保真度与信道自旋初态之间的关系. 结果表明, 平均保真度的大小只依赖于信道中自旋激发数的奇偶性. 通过比较在奇偶激发信道中获得的最大平均保真度, 构建了优化信道来提升量子态在自旋链中的传输质量. 进一步分析了纠缠在激发信道中的传输情况, 发现纠缠的传输质量不仅和信道中自旋激发的具体个数有关, 还取决于激发自旋的初始排列. 特别地, 当信道中自旋无激发或全部激发时, 纠缠传输的大小和持续时间都优于其他的激发信道. 上述研究结果有助于在实际系统中搭建适合量子态和纠缠传输的量子信道.The transfer of quantum states between distant nodes is one of the most fundamental tasks in quantum-information processing. Recent studies show that the antiferromagnetic spin chain initially prepared in a multi-excitation state can provide suitable pathways for quantum state transfer. In this paper, we investigate the quality of state transfer through a uniformly coupled antiferromagnetic spin chain where the initial state of the channel varies with the number of spin excitations. Firstly, by analyzing the dynamics of observables for the output qubit using the information-flux approach, the explicit relation about how the average fidelity of state transfer depends on the initial state of the spin channel is obtained. The results show that the average fidelity of state transfer through a multi-excitation spin channel only relates to the parity of the number of spin excitations in the channel. Then we compare the maximum average fidelity of state transfer through the odd-excitation with those through the even-excitation spin channels, and provide a simple criterion to optimize the quality of state transfer by choosing appropriate channels from the odd-excitation and the even-excitation channels. Compared with the previous studies which initialize the chains into the ground state of the ferromagnetic medium or the Nel state, the maximum average fidelity of state transfer is evidently enhanced by using the optimized channel. Moreover, we analyze the entanglement distribution through the channel having different number of spin excitations via the information-flux approach. It is found that the quality of entanglement distribution not only relates to the number of initial spin excitations present in the channel, but also depends on the initial ordering of these excited spins. The numerical results suggest that the amount of distributed entanglement and duration of distribution in the channel where all spins are down or up are larger than those in other excited channels. Based on these results, we can choose appropriate quantum channels for state transfer and entanglement distribution in practice.
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[1] Bose S 2003 Phys. Rev. Lett. 91 207901
[2] Christandl M, Datta N, Ekert A, Landahl A J 2004 Phys. Rev. Lett. 92 187902
[3] Albanese C, Christandl M, Datta N, Ekert A 2004 Phys. Rev. Lett. 93 230502
[4] Shi T, Li Y, Song Z, Sun C P 2005 Phys. Rev. A 71 032309
[5] Nikolopoulos G M, Petrosyan D, Lambropoulos P
[6] Franco C D, Paternostro M, Kim M S 2008 Phys. Rev. Lett. 101 230502
[7] Markiewicz M, Wiesniak M 2009 Phys. Rev. A 79 054304
[8] Maruyama K, Iitaka T, Nori F 2007 Phys. Rev. A 75 012325
[9] Zhang J, Shao B, Liu B Q 2011 Phys. Rev. A 84 012327
[10] Wang Z M, Shao B, Chang P, Zou J 2007 J. Phys. A 40 9067
[11] Zhang J, Shao B, Zou J, Li Q S 2011 Chin. Phys. B 20 100307
[12] Banchi L, Apollaro T J G, Cuccoli A, Vaia R, Verrucchi P 2010 Phys. Rev. A 82 052321
[13] Banchi L, Apollaro T J G, Cuccoli A, Vaia R, Verrucchi P 2011 New J. Phys. 13 123006
[14] Apollaro T J G, Banchi L, Cuccoli A, Vaia R, Verrucchi P 2012 Phys. Rev. A 85 052319
[15] Zeng T H, Shao B, Zou J 2009 Chin. Phys. Lett. 26 020313
[16] Cai J M, Zhou Z W, Guo G C 2006 Phys. Rev. A 74 022328
[17] Qin W, Li J L, Long G L 2015 Chin. Phys. B 24 040305
[18] He Z, Yao C M, Zou J 2013 Phys. Rev. A 88 044304
[19] Bayat A, Banchi L, Bose S, Verrucchi P 2011 Phys. Rev. A 83 062328
[20] Liu Y, Zhou D L 2014 Phys. Rev. A 89 062331
[21] Li J, Wu S H, Zhang W W, Xi X Q 2011 Chin. Phys. B 20 100308
[22] Wu S H, Hu M L, Li J, Xi X Q 2011 Acta Phys. Sin. 60 010302 (in Chinese) [吴世海, 胡明亮, 李季, 惠小强 2011 物理学报 60 010302]
[23] Zhang Y Q, Xu J B 2012 Chin. Phys. B 21 010304
[24] Hirjibehedin C F, Lutz C P, Heinrich A J 2006 Science 312 1021
[25] Heinrich A J, Gupta J A, Lutz C P, Eigler D M
[26] Wang Z M, Ma R S, C Allen Bishop, Gu Y J 2012 Phys. Rev. A 86 022330
[27] Bayat A, Bose S 2010 Adv. Math. Phys. 2010 127182
[28] Franco C D, Paternostro M, Palma G M, Kim M S 2007 Phys. Rev. A 76 042316
[29] Franco C D, Paternostro M, Kim M S 2010 Phys. Rev. A 81 022319
[30] Apollaro T J G, Cuccoli A, Franco C D, Paternostro M, Plastina F, Verrucchi P 2010 New J. Phys. 12 083046
[31] Horodecki M, Horodecki P, Horodecki R 1999 Phys. Rev. A 60 1888
[32] Bennett C H, Brassard G, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[33] Xi Y X, Shan C J, Huang Y X 2014 Acta Phys. Sin. 63 110305 (in Chinese) [郗玉兴, 单传家, 黄燕霞 2014 物理学报 63 110305]
[34] Jennewein T, Simon C, Weihs G, Weinfurter H, Zeilinger A 2000 Phys. Rev. Lett. 84 4729
[35] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[36] Simon J, Bakr W S, Ma R, Tai M E, Preiss P M, Greiner M 2011 Nature 472 307
[37] Weitenberg C, Endres M, Sherson J F, Cheneau M, Schau P, Fukuhara T, Bloch I, Kuhr S 2011 Nature 471 319
[38] Zhao X, Zhao X D, Jing H 2013 Acta Phys. Sin. 62 060302 (in Chinese) [赵旭, 赵兴东, 景辉 2013 物理学报 62 060302]
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