多环境影响下的量子导引动力学
|
摘要
本文基于与各自的两层环境相互作用的两量子比特系统,详细考察了强、弱耦合体系下第二层环境的腔个数N和两层环境间的耦合系数κ对量子导引动力学的影响,研究发现:随着N和κ的增加,量子导引不仅可以出现振荡现象,而且存活时间和量值都能得到一定程度地提高。为了抑制环境退相干,我们还讨论了量子弱测量和测量反转操作对量子导引动力学的调制作用,结果表明弱测量方法可以有效地保护量子导引。
The effects of the second-layer environments' cavity number N and the coupling strength κ between two-layer environments on the dynamics of quantum steering have been explored in detail for the weak and strong coupling regimes in this paper based on a quantum system consisting of two qubits, each interacting independently with its own two-layer environments.It has been shown that,with the increase in N and κ, quantum steering presents the oscillation phenomenon, and the survival time and values of which can be improved to some extent.In order to suppress the environmental decoherence, we discuss further the manipulation of quantum weak measurement and measurement reversal on quantum steering.The result shows that quantum steering can be protected effectively by the weak measurement method.
The effects of the second-layer environments' cavity number N and the coupling strength κ between two-layer environments on the dynamics of quantum steering have been explored in detail for the weak and strong coupling regimes in this paper based on a quantum system consisting of two qubits, each interacting independently with its own two-layer environments.It has been shown that,with the increase in N and κ, quantum steering presents the oscillation phenomenon, and the survival time and values of which can be improved to some extent.In order to suppress the environmental decoherence, we discuss further the manipulation of quantum weak measurement and measurement reversal on quantum steering.The result shows that quantum steering can be protected effectively by the weak measurement method.
引文
[1] Einstein A,Podolsky B,Rosen N.Can Quantum-mechanical Description of Physical Reality be Considered Complete?[J].Phys Rev,1935,47(10):777.DOI:10.1103/PhysRev.47.777.
[2] Schr?dinger E.Discussion of Probability Relations Between Separated Systems[C].Math Proc Cambridge Philos Soc,1935,31(4):555-563.DOI:10.1017/S0305004100013554.
[3] Schr?dinger E.Probability Relations Between Separated Systems[J].Math Proc Cambridge Philos Soc,1936,32(3):446-452.DOI:10.1017/S0305004100019137.
[4] Genovese M.Research on Hidden Variable Theories:A Review of Recent Progresses[J].Phys Rep,2005,413(6):319-396.DOI:10.1016/j.physrep.2005.03.003.
[5] Capasso V,Fortunato D,Selleri F.Sensitive Observables of Quantum Mechanics[J].Int J Theor Phys,1973,7(5):319-326.DOI:10.1007/BF00669912.
[6] Wiseman H M,Jones S J,Doherty A C.Steering,Entanglement,Nonlocality,and the Einstein-Podolsky-Rosen Paradox[J].Phys Rev Lett,2007,98(14):140402.DOI:10.1103/PhysRevLett.98.140402.
[7] Jones S J,Wiseman H M,Doherty A C.Entanglement,Einstein-podolsky-rosen Correlations,Bell Nonlocality,and Steering[J].Phys Rev A,2007,76(5):052116.DOI:10.1103/PHYSREVA.76.052116.
[8] Skrzypczyk P,Cavalcanti D.Maximal Randomness Generation from Steering Inequality Violations Using Qudits[J].Physical Review Letters,2018,120(26):260401.DOI:10.1103/PhysRevLett.120.260401.
[9] Saunders D J,Jones S J,Wiseman H M,et al.Experimental EPR-steering using Bell-local States[J].Nat Phys,2010,6(11):845.DOI:10.1038/nphys2094.
[10] Chen P W,Manirul Ali M,Chen S H.Enhanced Quantum Nonlocality Induced by the Memory of a Thermal-squeezed Environment[J].J Phys A Math Theor,2016,49(39):395302.DOI:10.1088/1751-8113/49/39/395302.
[11] Bowles J,Vértesi T,Quintino M T,et al.One-way Einstein-podolsky-rosen Steering[J].Phys Rev Lett,2014,112(20):200402.DOI:10.1103/PhysRevLett.112.200402.
[12] Walk N,Hosseni S,Geng J,et al.Experimental Demonstration of Gaussian Protocols for One-sided Device-independent Quantum Key Distribution[J].Optica,2016,3(6):634.DOI:10.1364/OPTICA.3.000634.
[13] Reid M D.Signifying Quantum Benchmarks for Qubit Teleportation and Secure Communication using Einstein-Podolsky-Rosen Steering Inequalities[J].Phys Rev A,2013,88(6):062338.DOI:10.1103/PhysRevA.88.062338.
[14] Kogias I,Skrzypczyk P,Cavalcanti D,et al.Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems[J].Phys Rev Lett,2015,115(21):210401.DOI:10.1103/PhysRevLett.115.210401.
[15] He Q,Rosales-Zárate L,Adesso G,et al.Secure Continuous Variable Teleportation and Einstein-Podolsky-Rosen Steering[J].Phys Rev Lett,2015,115(18):180502.DOI:10.1103/PhysRevLett.115.180502.
[16] Kogias I,Lee A R,Ragy S,et al.Quantification of Gaussian Quantum Steering[J].Phys Rev Lett,2015,114(6):060403.DOI:10.1103/PhysRevLett.114.060403.
[17] Deng X,Xiang Y,Tian C,et al.Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States[J].Phys Rev Lett,2017,118(23):230501.DOI:10.1103/PhysRevLett.11 8.230501.
[18] Sun K,Ye X J,Xu J S,et al.Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering[J].Phys Rev Lett,2016,116(16):160404.DOI:10.1103/PhysRevLett.116.160404.
[19] Wasak T,Chwedeńczuk J.Bell Inequality,Einstein-Podolsky-Rosen Steering,and Quantum Metrology with Spinor Bose-Einstein Condensates[J].Phys Rev Lett,2018,120(14):140406.DOI:10.1103/PhysRevLett.120.140 406.
[20] Zeng Q,Wang B,Li P,et al.Experimental High-Dimensional Einstein-Podolsky-Rosen Steering[J].Phys Rev Lett,2018,120(3):030401.DOI:10.1103/PhysRevLett.120.030401.
[21] Wang M,Gong Q,Ficek Z,et al.Role of Thermal Noise in Tripartite Quantum Steering[J].Phys Rev A,2014,90(2):0 23801.DOI:10.1103/PhysRevA.90.023801.
[22] Hu X,Fan H.Effect of Local Channels on Quantum Steering Ellipsoids[J].Phys Rev A,2015,91(2):022301.DOI:10.1103/PhysRevA.91.022301.
[23] Sun W Y,Wang D,Shi J D,et al.Exploration Quantum Steering,Nonlocality and Entanglement of Two-qubit X-state in Structured Reservoirs[J].Sci Rep,2017,7:39651.DOI:10.1038/srep39651.
[24] Li J,Zhu S Y.Einstein-Podolsky-Rosen Steering and Bell Nonlocality of Two Macroscopic Mechanical Oscillators in Optomechanical Systems[J].Phys Rev A,2017,96(6):062115.DOI:10.1103/PhysRevA.96.062115.
[25] Sun Z,Xu X Q,Liu B.Creation of Quantum Steering by Interaction with a Common Bath[J].Phys Rev A,2018,97(5):052309.DOI:10.1103/PhysRevA.97.052309.
[26] Zhong W,Cheng G,Hu X.One-way Einstein-Podolsky-Rosen Steering with the Aid of the Thermal Noise in a Correlated Emission Laser[J].Laser Phys Lett,2018,15(6):065204.DOI:10.1088/1612-202X/aab9ce.
[27] Wang J,Cao H,Jing J,et al.Gaussian Quantum Steering and Its Asymmetry in Curved Spacetime[J].Phys Rev D,2016,93(12):125011.DOI:10.1103/PhysRevD.93.125011.
[28] Wang J,Jing J,Fan H.Monogamy of Einstein-Podolsky-Rosen Steering in the Background of an Asymptotically Flat Black Hole[J].ANN PHYS-BERLIN,2018,530(3):1700261.DOI:10.1002/andp.201700261.
[29] Hanson R,Dobrovitski V V,Feiguin A E,et al.Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath[J].Sci,2008,320(5874):352-355.DOI:10.1126/science.1155400.
[30] Fruchtman A,Lovett B W,Benjamin S C,et al.Quantum Dynamics in a Tiered Non-Markovian Environment[J].New J Phys,2015,17(2):023063.DOI:10.1088/1367-2630/17/2/023063.
[31] Li J Q,Bai L,Liang J Q.Entropic Uncertainty Relation Under Multiple Bosonic Reservoirs with Filtering Operator[J].Quantum In Processing,2018,17(8):206.DOI:10.1007/s11128-018-1973-z.
[32] Ku H Y,Chen S L,Budroni C,et al.Einstein-Podolsky-Rosen Steering:Its Geometric Quantification and Witness[J].Phys Rev A,2018,97(2):022338.DOI:10.1103/PhysRevA.97.022338.
[33] Schneeloch J,Broadbent C J,Walborn S P,et al.Einstein-Podolsky-Rosen Steering Inequalities from Entropic Uncertainty Relations[J].Phys Rev A,2013,87(6):062103.DOI:10.1103/PhysRevA.87.062103.
[34] Riccardi A,Macchiavello C,Maccone L.Multipartite Steering Inequalities based on Entropic Uncertainty Relations[J].Phys Rev A,2018,97(5):052307.DOI:10.1103/PhysRevA.97.052307.
[35] Xu K,Zhang Y J,Xia Y J,et al.Hierarchical-environment-assisted Non-Markovian Speedup Dynamics Control[J].Phys Rev A,2018,98(2):022114.DOI:10.1103/PhysRevA.98.022114.
[36] Bellomo B,Franco R L,Compagno G.Non-Markovian Effects on the Dynamics of Entanglement[J].Phys Rev Lett,2007,99(16):160502.DOI:10.1103/PhysRevLett.99.160502.
[37] Facchi P,Lidar D A,Pascazio S.Unification of Dynamical Decoupling and the Quantum Zeno Dffect[J].Phys Rev A,2004,69(3):032314.DOI:10.1103/PhysRevA.69.032314.
[38] Calderbank A R,Shor P W.Good Quantum Error-correcting Codes Exist[J].Phys Rev A,1996,54(2):1098.DOI:10.11 03/PhysRevA.54.1098.
[39] Katz N,Neeley M,Ansmann M,et al.Reversal of the Weak Measurement of a Quantum State in a Superconducting Phase Qubit[J].Phys Rev lett,2008,101(20):200401.DOI:10.1103/PhysRevLett.101.200401.
[40] Zhi H,Chun-Mei Y.Enhancing the Precision of Phase Estimation by Weak Measurement and Quantum Measurement Reversal[J].Chinese Phys B,2014,23(11):110601.DOI:10.1088/1674-1056/23/11/110601.
[2] Schr?dinger E.Discussion of Probability Relations Between Separated Systems[C].Math Proc Cambridge Philos Soc,1935,31(4):555-563.DOI:10.1017/S0305004100013554.
[3] Schr?dinger E.Probability Relations Between Separated Systems[J].Math Proc Cambridge Philos Soc,1936,32(3):446-452.DOI:10.1017/S0305004100019137.
[4] Genovese M.Research on Hidden Variable Theories:A Review of Recent Progresses[J].Phys Rep,2005,413(6):319-396.DOI:10.1016/j.physrep.2005.03.003.
[5] Capasso V,Fortunato D,Selleri F.Sensitive Observables of Quantum Mechanics[J].Int J Theor Phys,1973,7(5):319-326.DOI:10.1007/BF00669912.
[6] Wiseman H M,Jones S J,Doherty A C.Steering,Entanglement,Nonlocality,and the Einstein-Podolsky-Rosen Paradox[J].Phys Rev Lett,2007,98(14):140402.DOI:10.1103/PhysRevLett.98.140402.
[7] Jones S J,Wiseman H M,Doherty A C.Entanglement,Einstein-podolsky-rosen Correlations,Bell Nonlocality,and Steering[J].Phys Rev A,2007,76(5):052116.DOI:10.1103/PHYSREVA.76.052116.
[8] Skrzypczyk P,Cavalcanti D.Maximal Randomness Generation from Steering Inequality Violations Using Qudits[J].Physical Review Letters,2018,120(26):260401.DOI:10.1103/PhysRevLett.120.260401.
[9] Saunders D J,Jones S J,Wiseman H M,et al.Experimental EPR-steering using Bell-local States[J].Nat Phys,2010,6(11):845.DOI:10.1038/nphys2094.
[10] Chen P W,Manirul Ali M,Chen S H.Enhanced Quantum Nonlocality Induced by the Memory of a Thermal-squeezed Environment[J].J Phys A Math Theor,2016,49(39):395302.DOI:10.1088/1751-8113/49/39/395302.
[11] Bowles J,Vértesi T,Quintino M T,et al.One-way Einstein-podolsky-rosen Steering[J].Phys Rev Lett,2014,112(20):200402.DOI:10.1103/PhysRevLett.112.200402.
[12] Walk N,Hosseni S,Geng J,et al.Experimental Demonstration of Gaussian Protocols for One-sided Device-independent Quantum Key Distribution[J].Optica,2016,3(6):634.DOI:10.1364/OPTICA.3.000634.
[13] Reid M D.Signifying Quantum Benchmarks for Qubit Teleportation and Secure Communication using Einstein-Podolsky-Rosen Steering Inequalities[J].Phys Rev A,2013,88(6):062338.DOI:10.1103/PhysRevA.88.062338.
[14] Kogias I,Skrzypczyk P,Cavalcanti D,et al.Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems[J].Phys Rev Lett,2015,115(21):210401.DOI:10.1103/PhysRevLett.115.210401.
[15] He Q,Rosales-Zárate L,Adesso G,et al.Secure Continuous Variable Teleportation and Einstein-Podolsky-Rosen Steering[J].Phys Rev Lett,2015,115(18):180502.DOI:10.1103/PhysRevLett.115.180502.
[16] Kogias I,Lee A R,Ragy S,et al.Quantification of Gaussian Quantum Steering[J].Phys Rev Lett,2015,114(6):060403.DOI:10.1103/PhysRevLett.114.060403.
[17] Deng X,Xiang Y,Tian C,et al.Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States[J].Phys Rev Lett,2017,118(23):230501.DOI:10.1103/PhysRevLett.11 8.230501.
[18] Sun K,Ye X J,Xu J S,et al.Experimental Quantification of Asymmetric Einstein-Podolsky-Rosen Steering[J].Phys Rev Lett,2016,116(16):160404.DOI:10.1103/PhysRevLett.116.160404.
[19] Wasak T,Chwedeńczuk J.Bell Inequality,Einstein-Podolsky-Rosen Steering,and Quantum Metrology with Spinor Bose-Einstein Condensates[J].Phys Rev Lett,2018,120(14):140406.DOI:10.1103/PhysRevLett.120.140 406.
[20] Zeng Q,Wang B,Li P,et al.Experimental High-Dimensional Einstein-Podolsky-Rosen Steering[J].Phys Rev Lett,2018,120(3):030401.DOI:10.1103/PhysRevLett.120.030401.
[21] Wang M,Gong Q,Ficek Z,et al.Role of Thermal Noise in Tripartite Quantum Steering[J].Phys Rev A,2014,90(2):0 23801.DOI:10.1103/PhysRevA.90.023801.
[22] Hu X,Fan H.Effect of Local Channels on Quantum Steering Ellipsoids[J].Phys Rev A,2015,91(2):022301.DOI:10.1103/PhysRevA.91.022301.
[23] Sun W Y,Wang D,Shi J D,et al.Exploration Quantum Steering,Nonlocality and Entanglement of Two-qubit X-state in Structured Reservoirs[J].Sci Rep,2017,7:39651.DOI:10.1038/srep39651.
[24] Li J,Zhu S Y.Einstein-Podolsky-Rosen Steering and Bell Nonlocality of Two Macroscopic Mechanical Oscillators in Optomechanical Systems[J].Phys Rev A,2017,96(6):062115.DOI:10.1103/PhysRevA.96.062115.
[25] Sun Z,Xu X Q,Liu B.Creation of Quantum Steering by Interaction with a Common Bath[J].Phys Rev A,2018,97(5):052309.DOI:10.1103/PhysRevA.97.052309.
[26] Zhong W,Cheng G,Hu X.One-way Einstein-Podolsky-Rosen Steering with the Aid of the Thermal Noise in a Correlated Emission Laser[J].Laser Phys Lett,2018,15(6):065204.DOI:10.1088/1612-202X/aab9ce.
[27] Wang J,Cao H,Jing J,et al.Gaussian Quantum Steering and Its Asymmetry in Curved Spacetime[J].Phys Rev D,2016,93(12):125011.DOI:10.1103/PhysRevD.93.125011.
[28] Wang J,Jing J,Fan H.Monogamy of Einstein-Podolsky-Rosen Steering in the Background of an Asymptotically Flat Black Hole[J].ANN PHYS-BERLIN,2018,530(3):1700261.DOI:10.1002/andp.201700261.
[29] Hanson R,Dobrovitski V V,Feiguin A E,et al.Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath[J].Sci,2008,320(5874):352-355.DOI:10.1126/science.1155400.
[30] Fruchtman A,Lovett B W,Benjamin S C,et al.Quantum Dynamics in a Tiered Non-Markovian Environment[J].New J Phys,2015,17(2):023063.DOI:10.1088/1367-2630/17/2/023063.
[31] Li J Q,Bai L,Liang J Q.Entropic Uncertainty Relation Under Multiple Bosonic Reservoirs with Filtering Operator[J].Quantum In Processing,2018,17(8):206.DOI:10.1007/s11128-018-1973-z.
[32] Ku H Y,Chen S L,Budroni C,et al.Einstein-Podolsky-Rosen Steering:Its Geometric Quantification and Witness[J].Phys Rev A,2018,97(2):022338.DOI:10.1103/PhysRevA.97.022338.
[33] Schneeloch J,Broadbent C J,Walborn S P,et al.Einstein-Podolsky-Rosen Steering Inequalities from Entropic Uncertainty Relations[J].Phys Rev A,2013,87(6):062103.DOI:10.1103/PhysRevA.87.062103.
[34] Riccardi A,Macchiavello C,Maccone L.Multipartite Steering Inequalities based on Entropic Uncertainty Relations[J].Phys Rev A,2018,97(5):052307.DOI:10.1103/PhysRevA.97.052307.
[35] Xu K,Zhang Y J,Xia Y J,et al.Hierarchical-environment-assisted Non-Markovian Speedup Dynamics Control[J].Phys Rev A,2018,98(2):022114.DOI:10.1103/PhysRevA.98.022114.
[36] Bellomo B,Franco R L,Compagno G.Non-Markovian Effects on the Dynamics of Entanglement[J].Phys Rev Lett,2007,99(16):160502.DOI:10.1103/PhysRevLett.99.160502.
[37] Facchi P,Lidar D A,Pascazio S.Unification of Dynamical Decoupling and the Quantum Zeno Dffect[J].Phys Rev A,2004,69(3):032314.DOI:10.1103/PhysRevA.69.032314.
[38] Calderbank A R,Shor P W.Good Quantum Error-correcting Codes Exist[J].Phys Rev A,1996,54(2):1098.DOI:10.11 03/PhysRevA.54.1098.
[39] Katz N,Neeley M,Ansmann M,et al.Reversal of the Weak Measurement of a Quantum State in a Superconducting Phase Qubit[J].Phys Rev lett,2008,101(20):200401.DOI:10.1103/PhysRevLett.101.200401.
[40] Zhi H,Chun-Mei Y.Enhancing the Precision of Phase Estimation by Weak Measurement and Quantum Measurement Reversal[J].Chinese Phys B,2014,23(11):110601.DOI:10.1088/1674-1056/23/11/110601.