量子纠缠态的远程制备
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摘要
量子信息学是二十世纪八十年代发展起来的,由量子力学和信息科学相结合而形成的一门新兴学科,主要包括量子通信和量子计算两个方面。由于量子信息潜在的应用价值(例如:可能给现有的信息产业带来划时代的革命)和重大的科学意义,正引起各方面越来越多的关注。
在量子信息学中,纠缠态是其最基本的要素,而以它为基础的一些研究方向如量子隐形传态,纠缠态的制备等也决定着量子信息网络能否最终实现。到目前为止,以上课题都取得了重要的突破但随着量子信息学往更深层次的发展,如何更加准确,更加节省资源的制备和传输纠缠态也逐渐成了量子信息学中急需解决的一个问题,所以在本论文中,主要将探索一种新的纠缠态制备方案:远程态制备。本文主要内容为:
1.提出了用三对最大的和非最大两粒子纠缠态作为量子通道远程制备一个三粒子纠缠态,此方案的优点在于其节省了更多的经典资源。
2.利用腔QED技术,提出了远程制备一个单原子态和一个两原子纠缠态。其优点在于,此方案只需要一个经典比特和一次测量,减少了操作步骤和资源。
Quantum Information is a new subject combined with Quantum Mechanics and Information Science. For its great applied potential in many fields, Quantum Information has received more and more attention.Entangled state plays a most essential role in Quantum Information. What's more, quantum teleportation and remote state preparation which are based on the entangled state determine the realization of Quantum Information Web. Although all these mentioned subjects have gained breakthrough, the pressing problem that how we can prepare remote state with a more accurate and saving way calls for solvability.This dissertation mainly includes the following works:1 Introduce the generation of three particles entangled state which uses three pairs maximally entangled state and nonmaximally entangled state. The advantage of this scheme is that it can save more classical resource.2 Based on the cavity QED techniques, we proposed a faithful scheme to prepare remote state of a single-atom state and a two-atom entangled state. This scheme has an exciting merit that only one classical bit and one single-atom state measurement is needed for the remote state preparation of multi-atom entangled state.
在量子信息学中,纠缠态是其最基本的要素,而以它为基础的一些研究方向如量子隐形传态,纠缠态的制备等也决定着量子信息网络能否最终实现。到目前为止,以上课题都取得了重要的突破但随着量子信息学往更深层次的发展,如何更加准确,更加节省资源的制备和传输纠缠态也逐渐成了量子信息学中急需解决的一个问题,所以在本论文中,主要将探索一种新的纠缠态制备方案:远程态制备。本文主要内容为:
1.提出了用三对最大的和非最大两粒子纠缠态作为量子通道远程制备一个三粒子纠缠态,此方案的优点在于其节省了更多的经典资源。
2.利用腔QED技术,提出了远程制备一个单原子态和一个两原子纠缠态。其优点在于,此方案只需要一个经典比特和一次测量,减少了操作步骤和资源。
Quantum Information is a new subject combined with Quantum Mechanics and Information Science. For its great applied potential in many fields, Quantum Information has received more and more attention.Entangled state plays a most essential role in Quantum Information. What's more, quantum teleportation and remote state preparation which are based on the entangled state determine the realization of Quantum Information Web. Although all these mentioned subjects have gained breakthrough, the pressing problem that how we can prepare remote state with a more accurate and saving way calls for solvability.This dissertation mainly includes the following works:1 Introduce the generation of three particles entangled state which uses three pairs maximally entangled state and nonmaximally entangled state. The advantage of this scheme is that it can save more classical resource.2 Based on the cavity QED techniques, we proposed a faithful scheme to prepare remote state of a single-atom state and a two-atom entangled state. This scheme has an exciting merit that only one classical bit and one single-atom state measurement is needed for the remote state preparation of multi-atom entangled state.
引文
[1] 李承祖等,量子通信和量子计算,国防科技大学出版社(2001)第一版
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[68] S.Bose, et al, Purification via entanglement swapping and conserve entanglement, Phys. Rev. A 60, 194(1999).
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[71] Jian-Wei Pan, et al, Nature( London), 430, 54 (2004).
[72] A. Zeilinger, et al, Three-Particle Entanglements from Two Entangled Pairs Phys. Rev. Lett. 78, 3031(1997).
[73] Jian-Wei Pan, Dik Bouwmeester, Matthew Daniell, Harald Weinflxreter, and Anton Zeilinger, Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement, Nature(London), 403,515(2000).
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[90] S. Shi, et al, J. Opt. B: Quantum Semiclassical Opt. 4, 380(2002).
[91] G. A. Paris, et al, J. Opt. B: Quantum Semiclassical Opt.5, S534(2003).
[92] Jian-Wei Pan, et al, Phys. Rev. Lett. 94, 150501(2005).
[2] A. Barenco et al, Conditional Quantum Dynamics and Logic Gates, Phys. Rev. Lett. 74, 4083(1995).
[3] T. Sleator, et al, Realizable Universal Quantum Logic Gates, Phys. Rev. Lett. 74, 4087(1995).
[4] D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network, Nature(London) 390, 575(1997).
[5] J. I. Cirac, P. Zoller, H. J. Kimble and H. Mabuchi, Phys. Rev. Lett. 78, 3221(1997).
[6] Schrodinger, E. Naturwissenschaften, Phys. Rev. 23, 807(1935).
[7] A. Einstein, B. Podolsky, N. Rosen, Phys. Rev, 47, 777(1935).
[8] 石名俊,博士论文(中国科学技术大学,2000).
[9] Aspect A, et al. Experimental Test of Bell's Inequalities Using Time-Varying Analyzers, Phys. Rev. Lett. 49, 1804(1982).
[10] V. Vedral, et al, Quantifying Entanglement, Phys. Rev. Lett. 78, 2275(1997).
[11] C. H. Bennett, et al. Concentrating Partial Entanglement by Local Operations Phys. Rev. A 53, 2046(1996).
[12] C. H. Bennett, et al., LANL e-print quant-ph/9908073.
[13] D. M. Greenberger, M. Home, A. Zeilinger, Bell's Theorem, Quantum Theory, and Conception of the Universe, edited by M. Kafatos(Kluwer. Dordrecht) (1998).
[14] W. Dur, G. Vidal and J. I. Ciac, Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62, 062314 (2000).
[15] J. I. Cirac and P. Zoller, Phys. Rev. A 50, 2799 (R)(1994).
[16] J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
[17] E. Hagley, X. Maitre et al, Phys. Rev. Lett. 79, 1 (1997).
[18] F. Freyberger, Phys. Rev. A 1, 3347 (1995).
[19] G. C. Guo, Y. S. Zhang, Scheme for preparation of the state via quantum electrodynamics, Phys. Rev. A 65, 054302 (2002).
[20] GS Jin, S. S Li, S. L Feng, H. Z Zheng, Method for generaring maximallyv entangled states of multiple three-level atoms in cavity QED, Phys. Rev. A 69, 034302 (2004).
[21] S. B Zheng and G. C. Guo, Efficient Scheme for Two-Atom Entanglement and Quantum Information Processingin Cavity QED, Phys. Rev. Lett. 85 2392(2000).
[22] S. Osnaghi, P. Bertet, et al, Coherent Control of an Atomic Collision in a Cavity Phys. Rev. Lett. 87, 037902 (2001).
[23] G-P. Guo, C-F. Li, J. Li, and G-C. Guo, Scheme for the preparation of multiparticle entanglement in cavity QED, Phys, Rev. A 65, 042102 (2002).
[24] W. Dur, G. Vidal, and J. I. Cirac, e-print quant-ph/0005115.
[25] X. G. Wang, e-print quant-ph/0101013.
[26] 叶柳,博士论文(中国科学技术大学,2003).
[27] Dik Bouwmeester, Jian-Wei Pan, Matthew Daniell, Harald Weinfureter, and Anton Zeilinger, Observation of Three-Photon Gl-eenberger-Horne-Zeilinger Entanglement Phys. Rev, Lett. 82, 1345 (1999).
[28] Jian-Wei Pan, Matthew Daniell, Gregor Weihs, Anton Zeilinger, Experimental Demonstration of Four-Photon Entanglement and High-Fidelity Teleportation, Phys. Rev. Lett 86, 4435 (2001).
[29] W. K. Wootters and W. H. Zurek, Nature(London) 299, 802 (1982).
[30] H. Barnum, C. M. Caves, et al, Phys. Rev. Lett, 76, 2818 (1996).
[31] L. Davidovich, N. Zagury, M. Brune, J. M. Raimond, S. Haroche, Teleportation of an atomic state between two cavities using nonlocal microwave fields. Phys. Rev. A 50(2), 895(R)(1994).
[32] J. L. Cirac, A. S. Parkins, Schemes for atomic-state teleportation, Phys. Rev. A 50(6), 4441 (R)(1994).
[33] N. G. Almeida, L. P. Maia, C. J. Uillas-boas, One-cavity scheme for atomic-state teleportation through GHZ states, Phys. Lett. A, 241(4), 213(1998).
[34] S-B Zheng, G-C Guo, Teleportation of an unknown atomic state through the Rarnan atom-cavity-field interaction, Phys. Lett. A, 232(6), 171 (1997).
[35] S-B Zheng, Teleportation of atomic states via resonant atom-field interaction, J. Mod. Opt, 167(5), 111 (1999).
[36] 许雪梅、罗文东.利用V型三能级原子与光场Raman相互作用传送光场的福克叠加态.物理学报,48(12),2154～2157(1999).
[37] M. H. Y. Moussa, Teleportation of a cavity-radiation-field state: An alternative scheme, Phys. Rev. A 54(6), 4661(1996).
[38] 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).
[39] Bao-Sen Shi, et al, Probabilistic teleportation of two-particle entangled state, Phy. Lett. A. 268, 161(2000).
[40] J. M. Liu, et al, Remote preparation of a two-particle entangled state, Phys. Lett. A 316, 159 (2003).
[41] Dai Hong-Yi, et al, Probabilistic teleportation of an unknown entangled state of two three-level particles using a partially entangled state of three three-level particles, Phys Lett A. 323, 360 (2004).
[42] D. Bouwmeester, J. W. Pan, et al., Nature(London) 390, 575 (1997).
[43] D. Boschi, S. Branca, et al, Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels, Phys. Rev. Lett. 80, 1121(1998).
[44] A. Furusawa, J. L. Sorensen, Science(London), 282, 706(1998).
[45] C. H. Bennett, et al, Remote state preparation, Phys. Rev. Lett. 87, 07790(2001).
[46] A. K. Pati, Minimum classical bit for remote preparation and measurement of a qubit, Phys. Rev. A 63, 014302 (2001).
[47] H. K. Lo, Classical-Communication cost in distributed quantum-information processing: A qeneralization of quantum-communication Complexity, Phys. Rev. A 62, 012313(2000).
[48] Jin-Ming Liu,Y-U-Zhu Wang, Remote preparation of a two-particle entangled state, Phys. Lett. A 316, 159(2003).
[49] B. Zeng, P. Zhang, Remote-state preparation in higher dimension and the parallelizable manifold S~n-1, Phys. Rev. A 65, 022316(2002).
[50] I. Devetak, T. Berger, Low-Entanglement Remote State Preparation, Phys. Rev. Lett. 87, 197901(2001).
[51] D.W. Berry, B.C. Sanders, Optimal Remote State Preparation, Phys. Rev. Lett. 90, 057901(2003).
[52] P. Agrawal, P. Parashar, A. Pati, quant-ph/0304006.
[53] Y.F. Yu, J. Feng, M.S. Zhan, Preparing remotely two instances of quantum state, Phys. Lett. A 310, 329(2003).
[54] M.G.A. Paris, M. Cola, R. Bonifacio, J. Opt. B: Quantum Semiclassical Opt. 5, S360(2003).
[55] X.H. Peng, et al, Phys. Lett. A 306, 271(2003).
[56] Hoi-Kwong, Lo,Classical-communication cost in distribute quantum-information processing: A generalization of quantum-communication complexity Phys. Rev. A 62, 012313(1999).
[57]Ye-Liu, et al, Teleportation of a two-particle entangled state, Chinese Physics 10 (2001).
[58] Yang Chui-Ping, et al, A Proposal Telepoatation of three-particle Entanged State, CHIN. PHYS. LETT. 16, 628(1999).
[59] W-L Li, et al, Probabilistic teleportation and entanglement matching, Phys Rev A 61,034301(2000).
[60] Dai Hong-Yi, et al, Probabilistic Teleportation of an Unknown Two-Particle Three-Level Entangled State, CHIN.PHYS.LETT. 21, 604(2004).
[61] A. K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett. 67,661(1991).
[62] J.M.Raimond, et al, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565(2001).
[63] J.I. Cirac and P. Zoller, Preparation of macroscopic superpositions in many-atom systems, Phys. Rev. A 50, 2799(R)(1994).
[64] G..P. Guo, C. F. Li, J. Li and G.C. Guo, Phys. Rev. A 65, 042102(2002).
[65] B. Zeng, P. Zhang, Remote-state preparation in higher dimension and the parallelizable manifold S~n-1, Phys. Rev. A 65,022316(2002).
[66] X. H. Peng, et al., Experimental implementation of remote state preparation by nuclear magnetic resonance, Phys. Lett. A 306, 271(2003).
[67] L. Ye, and G C. Guo, J. Opt. Soc. Am. B 20, 97(2003).
[68] S.Bose, et al, Purification via entanglement swapping and conserve entanglement, Phys. Rev. A 60, 194(1999).
[69] J-C Hao, C-F Li, G-C Guo, Controlled dense coding using the Greenberger-Horne-Zeilinger state, Phys. Rev.A.V63, 054301(1999).
[70] Bao-Sen.Shi,Yun-Kun. Jiang,Guang-Can.Guo, Probabilistic teleporatation of two-particle entangled state, Phys. Lett. A. 268, 161(2000).
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