量子热纠缠信道和腔QED中的隐形传态研究
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摘要
本文主要讨论了一维伊辛模型中,均匀磁场和非均匀磁场中,量子的热纠缠和量子传输的保真度;以及利用腔QED来实现未知量子态的传输。
所谓量子隐形传态是指:将Alice的某个粒子的未知量子态传送到Bob处的另一个粒子上,使得这个粒子与原来Alice的粒子处在相同的状态上,这种传递只是粒子信息的传递而不是物质的传递,即传送的只是粒子的状态信息,而粒子本身并没有被传送。由于量子力学的不确定原理,我们不能精确地将原量子态的所有信息全部提取出来,所以就将原来量子态的所有信息分为经典信息和量子信息两部分,他们分别由经典通道和量子通道传送,根据这些信息,可以构造出原量子态的全貌。
本文提出利用伊辛链作为量子通道来传输两未知量子态,并讨论了传输的平均保真度。由于外界因素的影响,我们很难利用纠缠纯态作为量子通道,而更多的是以混合纠缠的形式出现,所以本文利用了一维热纠缠伊辛链作为量子信道,实现了两粒子态的远程传输,分析了外界磁场、温度、耦合系数对纠缠度和保真度的影响。
量子信息是以量子态为量子信息的载体,以对各种量子态的制备和操纵来实现量子信息的处理,腔量子电动力学装置是最重要和最有前景的一种。腔QED的主要思想是将俘获的原子约束在高品质腔中,把量子信息储存在原子能态上,由于腔内原子与腔模场耦合,导致原子间相互作用,产生态的演化,从而可以实现量子态的制备、操作和利用腔QED进行量子态的隐形传送。
在量子信息处理过程中,量子系统与周围环境相互作用总会破坏系统内部的相干演化,从而导致信息的丧失,因此,大多数方案都是尽可能地把系统和环境隔离开,然而,消相干是无法完全避免的,在以前的用腔QED进行量子信息处理的大多数方案中,腔只是作为存储器,而把腔作为量子信息处理的主要障碍之一是腔泄露这种消相干,因此,对光腔Q值的要求很高,现有技术难以实现。大失谐QED方案是一种有效克服光腔消相干现象的新型处理器方案,系统对强的耗散和热辐射不敏感,这样就大大降低了对光腔Q值的要求,利用该方案可以实现量子隐形传态,本文利用腔QED的大失谐作用,利用3个粒子W态的非最大纠缠作为量子通道,实现未知态的远程传输。
本文共分为四章,第一章主要介绍了量子隐形传送和量子信道的基本知识。本文的第二、第三章是我主要研究的工作。第二章讨论了伊辛模型中量子的热纠缠和量子隐形传送的保真度。第三章介绍了利用腔QED传送两未知粒子的隐形传态及传输的概率。第四章对未来量子信息的发展作了展望。
This thesis discusses the thermal entanglement and average fidelity in the two-qubit Ising model with a uniform and nonuniform magnetic field, respectively. We also discuss a feasible scheme to teleport two unknown atoms using non-maximally entangled states without Bell-state measurement by Cavity QED.
The original quantum teleportation means that the sender Alice transits an unknown qubit state to the distant receiver Bob. Note that what the special procedure transit is only the information of Alice's qubit state, while the original qubit remains in Alice's site, one cannot make exact copy and directly extract full information from the original state. Due to the uncertain principal of quantum mechanics, one cannot extract all information of the original quantum state exactly. Therefore, one divides all information into two parts: general information and quantum information. A classical channel informs general information and quantum information is informed by quantum channel. So, one can reconstruct all information of the original quantum state in the other place.
In this paper, we present a scheme to teleport two unknown quantum states with the Ising chain, we discuss the fidelity as well. Because of the environment's affection, we can hardly teleport information with pure entangled states. Therefore, a quantum channel is always represented by mix states. So in this paper, we teleport a two-particle entangled state through the channel of thermal mixed states in 1D Ising chain. We study the effect of the external magnetic field, temperature and coupling coefficient on the concurrence and fidelity.
Quantum information is based on the quantum state, of all the quantum state's preparation and operation to realize the management of the quantum information, cavity is the most important and promising hardware. The main idea is that we restrict the atom in high-Q cavity. We store the quantum information in the atom's energy state. As the atom interacts with the cavity, which leads to the interaction of the atoms and then make the state changed, and at last we realize the operation and preparation of quantum state. We can also use the cavity to realize the teleportation of unknown quantum state.
Of the quantum information's management, the quantum system interacts with the environment, so it destroys the quantum system and loses some of the information. Most schemes are put forward to separate the quantum system with the surroundings as possible as we can, but it cannot avoid the degradation. In previous schemes of using the cavity to deal with the quantum information, cavity only acts as the memorizer, and the obstacle of the information's management is the degradation. So it requires the high quality of the cavity, but it is difficult to realize. Now, with the detuned interaction, which can overcome the shortcomings of the cavity decay. It is not sensitive to the thermal field and the cavity decay, so it does not require very high quality of the cavity, we can teleport unknown quantum qubit by QED successfully. In this paper, we use the detuned interaction between atoms and atoms in cavity, with GHZ non-maximally entangled state as the quantum channel to teleport two unknown quantum states.
The paper is organized as follows: In the first chapter, we introduce the basic knowledge about the quantum teleportation and the quantum channel. The second and the third chapters are the main work we do. In the second chapter, we investigate the thermal entanglement and average fidelity in the two-qubit Ising model with a uniform and nonuniform magnetic field. In the third chapter, we propose a protocol for teleportation of two unknown atomic states using non-maximally entangled states on channel QED. And in the last chapter, we make some conclusion and foreground.
所谓量子隐形传态是指:将Alice的某个粒子的未知量子态传送到Bob处的另一个粒子上,使得这个粒子与原来Alice的粒子处在相同的状态上,这种传递只是粒子信息的传递而不是物质的传递,即传送的只是粒子的状态信息,而粒子本身并没有被传送。由于量子力学的不确定原理,我们不能精确地将原量子态的所有信息全部提取出来,所以就将原来量子态的所有信息分为经典信息和量子信息两部分,他们分别由经典通道和量子通道传送,根据这些信息,可以构造出原量子态的全貌。
本文提出利用伊辛链作为量子通道来传输两未知量子态,并讨论了传输的平均保真度。由于外界因素的影响,我们很难利用纠缠纯态作为量子通道,而更多的是以混合纠缠的形式出现,所以本文利用了一维热纠缠伊辛链作为量子信道,实现了两粒子态的远程传输,分析了外界磁场、温度、耦合系数对纠缠度和保真度的影响。
量子信息是以量子态为量子信息的载体,以对各种量子态的制备和操纵来实现量子信息的处理,腔量子电动力学装置是最重要和最有前景的一种。腔QED的主要思想是将俘获的原子约束在高品质腔中,把量子信息储存在原子能态上,由于腔内原子与腔模场耦合,导致原子间相互作用,产生态的演化,从而可以实现量子态的制备、操作和利用腔QED进行量子态的隐形传送。
在量子信息处理过程中,量子系统与周围环境相互作用总会破坏系统内部的相干演化,从而导致信息的丧失,因此,大多数方案都是尽可能地把系统和环境隔离开,然而,消相干是无法完全避免的,在以前的用腔QED进行量子信息处理的大多数方案中,腔只是作为存储器,而把腔作为量子信息处理的主要障碍之一是腔泄露这种消相干,因此,对光腔Q值的要求很高,现有技术难以实现。大失谐QED方案是一种有效克服光腔消相干现象的新型处理器方案,系统对强的耗散和热辐射不敏感,这样就大大降低了对光腔Q值的要求,利用该方案可以实现量子隐形传态,本文利用腔QED的大失谐作用,利用3个粒子W态的非最大纠缠作为量子通道,实现未知态的远程传输。
本文共分为四章,第一章主要介绍了量子隐形传送和量子信道的基本知识。本文的第二、第三章是我主要研究的工作。第二章讨论了伊辛模型中量子的热纠缠和量子隐形传送的保真度。第三章介绍了利用腔QED传送两未知粒子的隐形传态及传输的概率。第四章对未来量子信息的发展作了展望。
This thesis discusses the thermal entanglement and average fidelity in the two-qubit Ising model with a uniform and nonuniform magnetic field, respectively. We also discuss a feasible scheme to teleport two unknown atoms using non-maximally entangled states without Bell-state measurement by Cavity QED.
The original quantum teleportation means that the sender Alice transits an unknown qubit state to the distant receiver Bob. Note that what the special procedure transit is only the information of Alice's qubit state, while the original qubit remains in Alice's site, one cannot make exact copy and directly extract full information from the original state. Due to the uncertain principal of quantum mechanics, one cannot extract all information of the original quantum state exactly. Therefore, one divides all information into two parts: general information and quantum information. A classical channel informs general information and quantum information is informed by quantum channel. So, one can reconstruct all information of the original quantum state in the other place.
In this paper, we present a scheme to teleport two unknown quantum states with the Ising chain, we discuss the fidelity as well. Because of the environment's affection, we can hardly teleport information with pure entangled states. Therefore, a quantum channel is always represented by mix states. So in this paper, we teleport a two-particle entangled state through the channel of thermal mixed states in 1D Ising chain. We study the effect of the external magnetic field, temperature and coupling coefficient on the concurrence and fidelity.
Quantum information is based on the quantum state, of all the quantum state's preparation and operation to realize the management of the quantum information, cavity is the most important and promising hardware. The main idea is that we restrict the atom in high-Q cavity. We store the quantum information in the atom's energy state. As the atom interacts with the cavity, which leads to the interaction of the atoms and then make the state changed, and at last we realize the operation and preparation of quantum state. We can also use the cavity to realize the teleportation of unknown quantum state.
Of the quantum information's management, the quantum system interacts with the environment, so it destroys the quantum system and loses some of the information. Most schemes are put forward to separate the quantum system with the surroundings as possible as we can, but it cannot avoid the degradation. In previous schemes of using the cavity to deal with the quantum information, cavity only acts as the memorizer, and the obstacle of the information's management is the degradation. So it requires the high quality of the cavity, but it is difficult to realize. Now, with the detuned interaction, which can overcome the shortcomings of the cavity decay. It is not sensitive to the thermal field and the cavity decay, so it does not require very high quality of the cavity, we can teleport unknown quantum qubit by QED successfully. In this paper, we use the detuned interaction between atoms and atoms in cavity, with GHZ non-maximally entangled state as the quantum channel to teleport two unknown quantum states.
The paper is organized as follows: In the first chapter, we introduce the basic knowledge about the quantum teleportation and the quantum channel. The second and the third chapters are the main work we do. In the second chapter, we investigate the thermal entanglement and average fidelity in the two-qubit Ising model with a uniform and nonuniform magnetic field. In the third chapter, we propose a protocol for teleportation of two unknown atomic states using non-maximally entangled states on channel QED. And in the last chapter, we make some conclusion and foreground.
引文
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[5]C. H. Bennett, G. Brassard, etc., Teleporting an unknown quantum state via dual classical and Einstein- Podolsky- Rosen channels. Phys. Rev. Lett. 70: 1895 - 1899(1993)
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[7] M. Hillery, V. Buzek and A. Berthiaume, Quantum secret sharing. Phys. Rev. A. 59: 1829-1834(1999)
[8]S.B. Zheng, One step synthesis of multi-atom Greenberger-Home-Zeilingerstates shnirman. Phys. Rev. Lett. 87: 230404-230408(2001)
[9]J.K. Pachos, A. Beige, Decoherence-free dynamical and geometrical entangling phase gates. Phys. Rev. A, 69: 033817-033826 (2004)
[10]W. H. Zhang and L. Ye, Scheme to implement general economical phase-covariant telecloning. Phys. Lett. A, 353: 130-137(2006)
[11]Y. Q. Zhang, X. R. Jin, S. Zhang, Secret sharing of quantum information via entanglement swapping in cavity QED. Phys. Lett. A, 341: 380-384 (2005)
[12] L.Ye and L. B. Yu, Scheme for implementing quantum dense coding using tripartite entanglement in cavity QED. Phys. Lett. A, 346: 330-336(2005)
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[14]T. Sleator, H. Weinfurter, Realizable universal quantum logic gates. Phys. Rev. Lett. 74: 4087-4090(1995)
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[18] Wang Y F, Cao J P, Wang Y P, Tunable entanglement of two-qubit XY model with in-plane magnetic fields. Phys. Lett. A, 342: 375-380(2005)
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[20]Wang X G. Effects of anisotropy on thermal entanglement. Phys. Lett. A, 281: 101-104(2001)
[21] Yang G H, Gao W B, Zhou L, et al., The entanglement in anisotropic Heisenberg XYZ chain with inhomogeneous magnetic field. arXiv: quantum-ph/0602051
[22]Bennett C H, et al., Teleporting an unknown quantum state via dual classical and Einstein-podolsky-Rosen channels. Phys. Rev. Lett, 70: 1895(1993)
[23]Bennett C. H, and Wisenser S. J, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett, 69: 2881 - 2884 (1992)
[24]Ekert A. K, Quantum cryptography based on Bell's theorem. Phys. Rev. Lett. 67: 661 -663(1991)
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[22]E. Hagley, X. Maitre, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, S. Hroche, Generation of Einstein-Podolsky-Rosen Pairs of Atoms. Phys. Rev. Lett. 79: 1(1997)
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[2]G. F. Zhang and S. S. Li, Thermal entanglement in a two- spin- qutribut system under a nonuniform external magnetis field. Arxiv: quantum-ph/050914(2005).
[3]A. Peres, Separability criterion for density matrices, Phys. Rev. Lett. 77: 1413-1415(1996).
[4]A. R. Usha Devi, R. Prabhu, and A. K. Rajagopal, Characterizing multiparticle entanglement in symmetric N-Qubit states via negativity of covariance matrices Phys. Rev. Lett. 98: 060501(2007)
[5]C. H. Bennett, G. Brassard, etc., Teleporting an unknown quantum state via dual classical and Einstein- Podolsky- Rosen channels. Phys. Rev. Lett. 70: 1895 - 1899(1993)
[6]C. H. Bennett and S. J. Wiesner. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69: 2881 - 2884(1992)
[7] M. Hillery, V. Buzek and A. Berthiaume, Quantum secret sharing. Phys. Rev. A. 59: 1829-1834(1999)
[8]S.B. Zheng, One step synthesis of multi-atom Greenberger-Home-Zeilingerstates shnirman. Phys. Rev. Lett. 87: 230404-230408(2001)
[9]J.K. Pachos, A. Beige, Decoherence-free dynamical and geometrical entangling phase gates. Phys. Rev. A, 69: 033817-033826 (2004)
[10]W. H. Zhang and L. Ye, Scheme to implement general economical phase-covariant telecloning. Phys. Lett. A, 353: 130-137(2006)
[11]Y. Q. Zhang, X. R. Jin, S. Zhang, Secret sharing of quantum information via entanglement swapping in cavity QED. Phys. Lett. A, 341: 380-384 (2005)
[12] L.Ye and L. B. Yu, Scheme for implementing quantum dense coding using tripartite entanglement in cavity QED. Phys. Lett. A, 346: 330-336(2005)
[13] E. Hagley, X. Maitre, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, S. Hroche, Generation of Einstein- Podolsky- Rosen Pairs of Atoms. Phys. Rev. Lett. 79: 1-5(1997)
[14]T. Sleator, H. Weinfurter, Realizable universal quantum logic gates. Phys. Rev. Lett. 74: 4087-4090(1995)
[15]J. I. Ciarc, and P. Zoller, Quantum computations with cold trapped ions. Phys. Rev. Lett., 74: 4091-4094 (1995)
[16]M. A. Nielsen, E. Knill, & R. Laflamme, Complete quantum teleportation by nuclear magnetic resonance. arXiv: Quant-ph/9811020
[17]H. F. Wang, K. Sabre, Quantum teleportation in one-dimension quantum dots system. Phys. Lett. A, 421: 338-342( 2006)
[18] Wang Y F, Cao J P, Wang Y P, Tunable entanglement of two-qubit XY model with in-plane magnetic fields. Phys. Lett. A, 342: 375-380(2005)
[19]Hao X, Zhu S Q, Entanglement teleportation through 1D Heisenberg chain. Phys. Lett A, 338: 175-181 (2005)
[20]Wang X G. Effects of anisotropy on thermal entanglement. Phys. Lett. A, 281: 101-104(2001)
[21] Yang G H, Gao W B, Zhou L, et al., The entanglement in anisotropic Heisenberg XYZ chain with inhomogeneous magnetic field. arXiv: quantum-ph/0602051
[22]Bennett C H, et al., Teleporting an unknown quantum state via dual classical and Einstein-podolsky-Rosen channels. Phys. Rev. Lett, 70: 1895(1993)
[23]Bennett C. H, and Wisenser S. J, Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett, 69: 2881 - 2884 (1992)
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