腔QED纯化前后相位阻尼对量子传输的影响
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摘要
量子纠缠是量子力学最显著的特征之一,它在量子信息学的各个领域都具有重要的作用。量子纠缠态作为量子信息处理的基本物理资源,被广泛地应用于量子计算机,量子通信,量子隐形传态和量子密集编码等领域中,然而,一个处于纯纠缠态的系统不可避免地要与环境相互作用并导致消相干,使纯纠缠态变成混合态。使用这种混合纠缠态进行量子通信和量子计算将导致编码在态中的量子信息失真。为了避免信息的失真,把混合纠缠态尽可能地恢复成接近纯纠缠态或纯纠缠态,即纠缠态的纯化就成为了量子传输中的关键问题。本文以具有相位阻尼特征的二能级原子与双模光场耦合系统为研究对象,通过对该系统进行纠缠纯化,研究了纯化前后相位阻尼对量子信息传输保真度影响的差异,并获得了通过纯化后的信道进行传输的最大保真度。
本文将围绕量子传输和量子态的纯化做详细地讨论。首先在第二章介绍量子传输的基本理论,包括量子纠缠态的提出,量子纠缠态的定义,量子传输保真度的定义,退相干的物理起源,相位阻尼的物理实质。第三章介绍了量子态的几种纯化方案,包括采用局域POVM方法和局域CNOT操作等方案。第四章提出了原子与双模光场耦合系统的纯化方案,并分别对系统纯化前后量子传输保真度进行了研究。研究表明:通过调整两个量子逻辑门的旋转角度,可以有效地改进相位阻尼和失谐对量子传输保真度的影响,并且获得了通过纯化后的信道进行传输的最大保真度。
Entanglement is one of the most striking features of quantum mechanics, and plays key pole in quantum information science. Quantum entanglement, as a physical resource, lies at the heart of quantum computation, quantum communication, quantum teleportation, and quantum superdense-coding. However, a maximally entangled state prepared for quantum information processing which is inevitablly interact with the environment, will easily become into a non-maximally entangled state. With this non-maximally entangled state in quantum communication and computation, the informat--ion is distorted. To overcome the above obstacle, entanglement purification become critical in quantum teleportation. In this paper, with the feature of intrinsic decoherence , the system of atom inter--acting with two distinct optical cavities is discussed. It is also studied the differences on the effect of the phase decoherence rate on the fidelity between before and after the system purificiation.Then, the maximal fidelity of quantum teleportation can be achieved.
In this paper, quantum teleportation and entanglement purification will be discussed in detail. Firstly, some basic theories of quantum teleporation are introduced in chapter 2, including the presentation and definition of entangled states, the definition of fidelity, the physical source and matter of decoherence. In chapter 3, the methods of entanglement purification are introduced, including local Controlled-Not (CNOT) operation and local Positive Operator-Valued Measuer (POVM). In chapter 4, the entanglement purification protocol for the system of atom interacting with two distinct optical cavities is discussed. The fidelities before and after the system purification are studied. The results indicate that the effect of the phase decoherence rate and detuning parameter on the fidelity can be reduced by modifying two quantum logical gates.Then, maximal fidelity of quantum teleportation can be achieved
本文将围绕量子传输和量子态的纯化做详细地讨论。首先在第二章介绍量子传输的基本理论,包括量子纠缠态的提出,量子纠缠态的定义,量子传输保真度的定义,退相干的物理起源,相位阻尼的物理实质。第三章介绍了量子态的几种纯化方案,包括采用局域POVM方法和局域CNOT操作等方案。第四章提出了原子与双模光场耦合系统的纯化方案,并分别对系统纯化前后量子传输保真度进行了研究。研究表明:通过调整两个量子逻辑门的旋转角度,可以有效地改进相位阻尼和失谐对量子传输保真度的影响,并且获得了通过纯化后的信道进行传输的最大保真度。
Entanglement is one of the most striking features of quantum mechanics, and plays key pole in quantum information science. Quantum entanglement, as a physical resource, lies at the heart of quantum computation, quantum communication, quantum teleportation, and quantum superdense-coding. However, a maximally entangled state prepared for quantum information processing which is inevitablly interact with the environment, will easily become into a non-maximally entangled state. With this non-maximally entangled state in quantum communication and computation, the informat--ion is distorted. To overcome the above obstacle, entanglement purification become critical in quantum teleportation. In this paper, with the feature of intrinsic decoherence , the system of atom inter--acting with two distinct optical cavities is discussed. It is also studied the differences on the effect of the phase decoherence rate on the fidelity between before and after the system purificiation.Then, the maximal fidelity of quantum teleportation can be achieved.
In this paper, quantum teleportation and entanglement purification will be discussed in detail. Firstly, some basic theories of quantum teleporation are introduced in chapter 2, including the presentation and definition of entangled states, the definition of fidelity, the physical source and matter of decoherence. In chapter 3, the methods of entanglement purification are introduced, including local Controlled-Not (CNOT) operation and local Positive Operator-Valued Measuer (POVM). In chapter 4, the entanglement purification protocol for the system of atom interacting with two distinct optical cavities is discussed. The fidelities before and after the system purification are studied. The results indicate that the effect of the phase decoherence rate and detuning parameter on the fidelity can be reduced by modifying two quantum logical gates.Then, maximal fidelity of quantum teleportation can be achieved
引文
[1]M.A.Nielsen and I.L.Chuang,Quantum Computation and Quantum Information,Cambridge Univ.PRESS,2000
[2]C.H.Bennett,Quantum and Classical Information:Transmission and Computation.Phys.Today 48,24(1995)
[3]C.H.Bennett,G.Brassard,C,Crepeau,R.Jozsa,Peres and W.K.Wootters,Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.Phys.Rev.Lerr.70,1895(1993)
[4]C.H.Bennett and S.J.Wiesner,Comrnunication via one and two-particle operators on Einstein-Podolsky-Rosen states.Phys.Rev.Lerr.69,2881(1992)
[5]M.Hillery,V.Buzek and A.Berthiaume,Quanyum secret sharing.Phys.Rev.A59,1829(1999)
[6]Y.D.Zhang.Principles of Quantum Information Physics.科学出版社,北京,2005ISBN 7-03-016368-0..
[7]Schumacher B.Quantum coding.Phys.Rev.(A),1995,51(4):2738-2747
[8]Schumacher B.Sending entanglement through noisy quantum channels.Phys.Rev.(A),1996,54(4):2614-2628
[9]Schumacher B,Nielsen M A.Quantum data processing and error correction.Phys.Rev.(A),1996,54(4):2629-2635
[10]Jozsa R.Fidelity for mixed quantum states.J.Mod.Opt.1994,41(12):2315-2323.
[11]Duan Luming,Guo Guangcan.Phys.Rev.(A),1997,56(6):4466-4470
[12]WangXiangbin,Oh C H,Kwer LC.Bures fidelity of displaced squeezed thermal states.Phys.Rev.(A),1998,58(5):4186-4190.
[13]Horodecki,R.Horodecki,M.Information-theoretic aspects of inseparability of Mixed states,Phys.Rev.(A),1996,54(3):1838-1843.
[14]A.Einstein,B.Podolsky,and N.Rosen,Can quantum-mechanical description of physical reality be considered complete?Phys.Rev.1935,47:777-780.
[15]E.Schrodinger.Naturwissenschaften,1935,23:807.
[16]W.Dur,G..Vidal and J.I.Ciac,Three qubits can be entangled through noisy quantum channels[J],Phys.Rev.(A),1996,52(3):1688-1693.
[17]M.Greenberger,M.A.Horne,and A.Zeilinger.Bell's theorem without inequalities [J].Am.J.Phy.1990,58:1131.
[18]W.Dur,G..Vidal and J.I.Ciac,Three qubits can be entangled in two inequivalent ways[J],Phys.Rev.A,2000,62(6):062314.
[19]D.Bouwmeester,J.W.Pan,K.Mattle et al,Nature,1997;390:575
[20]M A Nielsen and I L Chuang.Quantum Computation and Quantum Information.C -ambridge:Cambridge University Press,2000.
[21]R Jozsa,J Mod Opt,1994,41:2315.
[22]X B Wang,et al.J Phys A;Math Gen,2000,33:4925.
[23]M B Ruskai,Rev Math Phys,1994,6(5A):l147
[24]C.H.Bennett and G.Braunstein,Phys.Rev.Lett,1993;70:1895.
[25]W K Wootters.PRL,1998,80:2245.
[26]逯怀新等.连续变量系统的量子信息处理与非定域性.见:量子力学新进展,第三集,曾谨言,裴寿镛,龙桂鲁主编,北京:清华大学出版社出版,2000.
[27]Knoll L,Orlowski A.Phys.Rev.1998,A58.883.
[28]A Quantum Information Science and Telenology Roadmap,Part1:Quantum Computation,Section6.9,§ 6.3,LA-UR-04-1778,2004.
[29]Lin Xiumin,Zhou Zhengwei,Guo Guangcan,et al.Scheme for implementing quantum dense coding via cavity QED[J].Phys.Lett.A,2003,313:351-355.
[30]Zheng Shibiao,Guo Guangcan.Efficient scheme for two-atom entanglement and quantum information processing in cavity QED[J],Phys.Rev.Lett.2000,85(11):2392-2395.
[31]BENNETT C H,BRASSARD G,CREPEAU C,et al.Teleporting and Unknown Quantum state via Dual Classical and Einstein-Podolsky-Rosen Channels[J].Phys Rev Lett,1993,70:1895-1899.
[32]BOUWMEASTER D,PAN J W,MATTLE K,et al.Experimental Quantum Teleportation[J].Nature,1997,390:575-579.
[33]于立志,龚仁山.通过四个纠缠态粒子来实现未知的三个纠缠态粒子的量子几率隐形传输[J].量子光学学报,2005,11(1):29-33.
[34]FURUSAWA A,SORENSEN J L,BRAUNSTEIN S L,et al.Unconditional Quantum Teleportation[J].Science,1998,282:706-709.
[35]Mark Hillery,Buzek V,Berthiaume A.Quantum secret sharing[J].Phys.Rev.A,1999,59(3):1829-1834.
[36]Bose S,Vedral V,Knight P L.Multiparticle generalization of entanglement swapping [J].Phys.Rev.A,1998,57(2):822-828.
[37]Feng Xunli,Gong Shangqing,Xu Zhizhan.Entanglement purification via controlled-controlled-NOT operations[J].Phys.Lett.A,2000,271:44-47.
[38]Romero J L,Roa L,Retamal J C,et al.Entanglement purification in cavity QED using local operations[J].Phys.Rev.A,2002,65(5):052319.
[39]BENNETT C H,BRASSARD G,POPESCU S,et al.Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels[J].Phys Rev Lett,1996,76:722-725.
[40]HORODECKIM,HORODECKI P,HORODECKI R.Inseparable Two Spin-1/2Density Matrices Can be Distilled to a Singlet Form[J].Phys Rev Lett,1997,78:574-577
[41]HORODECKIM,HORODECKI P,HORODECKIR.Mixed-state Entanglement and Eistillation:Is there a "Bound" Entanglement in Nature?[J].Phys Rev Lett,1998,80:5239-5240.
[42]BOSE S,VDDRAL V,KN IGHT P L.Purification via Entanglement Swapping and Conserved Entanglement[J].Phys Rev A,1999,60:194-197.
[43]J Preskill.Lecture Notes for Physcis 229:Quantum Information and Computation.CIT,1998,242-245.
[44]A Ekert,et al.Rev Mod Phys,1996,68:733.
[45]M A Nielsen and I L Chuang.Quantum Computation and Quantum Information.Cambridge;Cambridge Univ Press,25-26,159.
[46]ibid 216,637.
[47]P W Shor,Proc of the 35~(th)Annual Symposium on the Foundations of Computer science.edited by S Goldwasser.IEEE Computer Science,quantum ph/9508027.
[48]张永德.量子力学.北京:科学出版社,2003,189-197.
[49]P A M狄拉克.量子力学原理.北京:科学出版社,1965,9.
[50]BENNETT C H,BRASSARD G,CREPEAU C,et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J].Phys Rev Lett,1993,70:1895-1898.
[51]NIELSEN M A,CHUANG I L.Quantum computation and quantum information [M].Camb-ridge:Cambridge University Press.2000.
[52]BARENCO A,EKERT A K.Dense coding based on quantum entanglement[J].J Mod opt,1995,42:1253-1259.
[53]DEUTSCH D,EKERT A,JOZSA R,et al.Quantum privacy amplification and the security of quantum cryptography over noisy channels[J].Phys Rev Lett,1996,77:2818-2821.
[54]Charles H.Bennett,Gilles Brassard,Sandu Popescu,Benjamin Schumacher,John A.Smolin,and William K.Wootters.Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels[J].Phys.Rev.Lett.76,722(1996)..
[55]Charles H.Bennett,David P.Di Vicenzo,JohnA.Smolin,and William K.Wootters.Mixed-state entanglement and quantum error correction.Phys.Rev.A 54,3824(1996).
[56]Nicolas Gisin.Hidden quantum nonlocality revealed by local filters.Phys.Lett.A 210,151(1996).
[57]Micha Horodecki,Pawel Horodecki,and Ryszard Horodecki.General teleportation channel,singlet fraction,and quasidistillation.Phys.Rev.A 60,1888(1999).
[58]Romero.J.L,Roa.L,Retamal.J.C,and Saavedra.C,Entanglement purification in cavity QED using local operations.Phys.Rev.A 65,052319(2002)
[59]Xu.J.B and Li.S.B.Generation of maximally entangled mixed states of two atoms inside an optical cavity.Eur.Phys.J.D 35,553-560(2005);Gardiner.C.W.Quantum Noise.(Springer Verlag,Berlin,1991);Louisell.W.H,Quantum Statistics Properties of Radiation.(Wiley,New York,1973)
[60]Knoll L,Orlowski A.Distance between density operators:applications to the J-C model[J].Phys.Rev.A,1995,51 {2}:1622.
[2]C.H.Bennett,Quantum and Classical Information:Transmission and Computation.Phys.Today 48,24(1995)
[3]C.H.Bennett,G.Brassard,C,Crepeau,R.Jozsa,Peres and W.K.Wootters,Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.Phys.Rev.Lerr.70,1895(1993)
[4]C.H.Bennett and S.J.Wiesner,Comrnunication via one and two-particle operators on Einstein-Podolsky-Rosen states.Phys.Rev.Lerr.69,2881(1992)
[5]M.Hillery,V.Buzek and A.Berthiaume,Quanyum secret sharing.Phys.Rev.A59,1829(1999)
[6]Y.D.Zhang.Principles of Quantum Information Physics.科学出版社,北京,2005ISBN 7-03-016368-0..
[7]Schumacher B.Quantum coding.Phys.Rev.(A),1995,51(4):2738-2747
[8]Schumacher B.Sending entanglement through noisy quantum channels.Phys.Rev.(A),1996,54(4):2614-2628
[9]Schumacher B,Nielsen M A.Quantum data processing and error correction.Phys.Rev.(A),1996,54(4):2629-2635
[10]Jozsa R.Fidelity for mixed quantum states.J.Mod.Opt.1994,41(12):2315-2323.
[11]Duan Luming,Guo Guangcan.Phys.Rev.(A),1997,56(6):4466-4470
[12]WangXiangbin,Oh C H,Kwer LC.Bures fidelity of displaced squeezed thermal states.Phys.Rev.(A),1998,58(5):4186-4190.
[13]Horodecki,R.Horodecki,M.Information-theoretic aspects of inseparability of Mixed states,Phys.Rev.(A),1996,54(3):1838-1843.
[14]A.Einstein,B.Podolsky,and N.Rosen,Can quantum-mechanical description of physical reality be considered complete?Phys.Rev.1935,47:777-780.
[15]E.Schrodinger.Naturwissenschaften,1935,23:807.
[16]W.Dur,G..Vidal and J.I.Ciac,Three qubits can be entangled through noisy quantum channels[J],Phys.Rev.(A),1996,52(3):1688-1693.
[17]M.Greenberger,M.A.Horne,and A.Zeilinger.Bell's theorem without inequalities [J].Am.J.Phy.1990,58:1131.
[18]W.Dur,G..Vidal and J.I.Ciac,Three qubits can be entangled in two inequivalent ways[J],Phys.Rev.A,2000,62(6):062314.
[19]D.Bouwmeester,J.W.Pan,K.Mattle et al,Nature,1997;390:575
[20]M A Nielsen and I L Chuang.Quantum Computation and Quantum Information.C -ambridge:Cambridge University Press,2000.
[21]R Jozsa,J Mod Opt,1994,41:2315.
[22]X B Wang,et al.J Phys A;Math Gen,2000,33:4925.
[23]M B Ruskai,Rev Math Phys,1994,6(5A):l147
[24]C.H.Bennett and G.Braunstein,Phys.Rev.Lett,1993;70:1895.
[25]W K Wootters.PRL,1998,80:2245.
[26]逯怀新等.连续变量系统的量子信息处理与非定域性.见:量子力学新进展,第三集,曾谨言,裴寿镛,龙桂鲁主编,北京:清华大学出版社出版,2000.
[27]Knoll L,Orlowski A.Phys.Rev.1998,A58.883.
[28]A Quantum Information Science and Telenology Roadmap,Part1:Quantum Computation,Section6.9,§ 6.3,LA-UR-04-1778,2004.
[29]Lin Xiumin,Zhou Zhengwei,Guo Guangcan,et al.Scheme for implementing quantum dense coding via cavity QED[J].Phys.Lett.A,2003,313:351-355.
[30]Zheng Shibiao,Guo Guangcan.Efficient scheme for two-atom entanglement and quantum information processing in cavity QED[J],Phys.Rev.Lett.2000,85(11):2392-2395.
[31]BENNETT C H,BRASSARD G,CREPEAU C,et al.Teleporting and Unknown Quantum state via Dual Classical and Einstein-Podolsky-Rosen Channels[J].Phys Rev Lett,1993,70:1895-1899.
[32]BOUWMEASTER D,PAN J W,MATTLE K,et al.Experimental Quantum Teleportation[J].Nature,1997,390:575-579.
[33]于立志,龚仁山.通过四个纠缠态粒子来实现未知的三个纠缠态粒子的量子几率隐形传输[J].量子光学学报,2005,11(1):29-33.
[34]FURUSAWA A,SORENSEN J L,BRAUNSTEIN S L,et al.Unconditional Quantum Teleportation[J].Science,1998,282:706-709.
[35]Mark Hillery,Buzek V,Berthiaume A.Quantum secret sharing[J].Phys.Rev.A,1999,59(3):1829-1834.
[36]Bose S,Vedral V,Knight P L.Multiparticle generalization of entanglement swapping [J].Phys.Rev.A,1998,57(2):822-828.
[37]Feng Xunli,Gong Shangqing,Xu Zhizhan.Entanglement purification via controlled-controlled-NOT operations[J].Phys.Lett.A,2000,271:44-47.
[38]Romero J L,Roa L,Retamal J C,et al.Entanglement purification in cavity QED using local operations[J].Phys.Rev.A,2002,65(5):052319.
[39]BENNETT C H,BRASSARD G,POPESCU S,et al.Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels[J].Phys Rev Lett,1996,76:722-725.
[40]HORODECKIM,HORODECKI P,HORODECKI R.Inseparable Two Spin-1/2Density Matrices Can be Distilled to a Singlet Form[J].Phys Rev Lett,1997,78:574-577
[41]HORODECKIM,HORODECKI P,HORODECKIR.Mixed-state Entanglement and Eistillation:Is there a "Bound" Entanglement in Nature?[J].Phys Rev Lett,1998,80:5239-5240.
[42]BOSE S,VDDRAL V,KN IGHT P L.Purification via Entanglement Swapping and Conserved Entanglement[J].Phys Rev A,1999,60:194-197.
[43]J Preskill.Lecture Notes for Physcis 229:Quantum Information and Computation.CIT,1998,242-245.
[44]A Ekert,et al.Rev Mod Phys,1996,68:733.
[45]M A Nielsen and I L Chuang.Quantum Computation and Quantum Information.Cambridge;Cambridge Univ Press,25-26,159.
[46]ibid 216,637.
[47]P W Shor,Proc of the 35~(th)Annual Symposium on the Foundations of Computer science.edited by S Goldwasser.IEEE Computer Science,quantum ph/9508027.
[48]张永德.量子力学.北京:科学出版社,2003,189-197.
[49]P A M狄拉克.量子力学原理.北京:科学出版社,1965,9.
[50]BENNETT C H,BRASSARD G,CREPEAU C,et al.Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J].Phys Rev Lett,1993,70:1895-1898.
[51]NIELSEN M A,CHUANG I L.Quantum computation and quantum information [M].Camb-ridge:Cambridge University Press.2000.
[52]BARENCO A,EKERT A K.Dense coding based on quantum entanglement[J].J Mod opt,1995,42:1253-1259.
[53]DEUTSCH D,EKERT A,JOZSA R,et al.Quantum privacy amplification and the security of quantum cryptography over noisy channels[J].Phys Rev Lett,1996,77:2818-2821.
[54]Charles H.Bennett,Gilles Brassard,Sandu Popescu,Benjamin Schumacher,John A.Smolin,and William K.Wootters.Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels[J].Phys.Rev.Lett.76,722(1996)..
[55]Charles H.Bennett,David P.Di Vicenzo,JohnA.Smolin,and William K.Wootters.Mixed-state entanglement and quantum error correction.Phys.Rev.A 54,3824(1996).
[56]Nicolas Gisin.Hidden quantum nonlocality revealed by local filters.Phys.Lett.A 210,151(1996).
[57]Micha Horodecki,Pawel Horodecki,and Ryszard Horodecki.General teleportation channel,singlet fraction,and quasidistillation.Phys.Rev.A 60,1888(1999).
[58]Romero.J.L,Roa.L,Retamal.J.C,and Saavedra.C,Entanglement purification in cavity QED using local operations.Phys.Rev.A 65,052319(2002)
[59]Xu.J.B and Li.S.B.Generation of maximally entangled mixed states of two atoms inside an optical cavity.Eur.Phys.J.D 35,553-560(2005);Gardiner.C.W.Quantum Noise.(Springer Verlag,Berlin,1991);Louisell.W.H,Quantum Statistics Properties of Radiation.(Wiley,New York,1973)
[60]Knoll L,Orlowski A.Distance between density operators:applications to the J-C model[J].Phys.Rev.A,1995,51 {2}:1622.