多种环境下量子纠缠的调控研究
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摘要
量子信息学是量子力学和信息科学相结合而发展起来的新型交叉学科，其诞生和发展在科学和技术方面具有深远意义。与经典信息处理相比，量子信息处理具有无可比拟的优越性，例如量子计算速度能够指数倍地提升经典计算速度；绝对意义上的安全通讯可以通过量子保密通讯做到等等。众所周知，绝大部分量子信息处理过程的实现都离不开系统的量子关联。量子纠缠作为量子信息学众多重要研究内容里最为核心的物理资源，其发展决定了量子信息技术应用前景的广阔性。然而，由于系统和环境之间存在着不可避免的相互作用，最终会破坏整个系统的量子纠缠，进而限制量子纠缠在实际量子信息和量子计算中的应用。这种局域退相干过程也是量子计算机实现的主要障碍，因而研究开放系统中各种不同环境导致的量子纠缠动力学是必要且有意义的。本论文主要研究的内容有以下几个方面：
1.详细讨论了不同环境模型中Bell型纠缠态系统的纠缠动力学。通过建立三种不同的环境模型（单一热库模型、共同热库模型和独立热库模型），利用赝模理论的方法，分析比较了初始处于Bell型纠缠态系统的纠缠动力学特性，给出了系统纠缠保持较优的环境模型。特别地，当热库谱密度为光子禁带时，选择合适的参数使光子禁带为理想带隙，研究发现在上述三种不同的比特-环境退相干信道中，都会发生两比特纠缠俘获现象。对比不同退相干信道模型对比特间纠缠俘获现象的影响，我们给出获得较大纠缠俘获的条件。
2.主要研究了不同的退相干环境对原子系统量子关联动力学的影响。考虑两个初始具有量子关联的原子分别与两个独立的局域环境相互作用的物理模型。主要对比研究了四种典型的环境模型：单洛伦兹环境模型，平方洛伦兹环境模型，双洛伦兹环境模型和光子禁带模型。研究发现，在弱耦合机制下，当原子与赝模满足共振或者近共振条件时，原子的量子discord在单洛伦兹环境模型（光子禁带模型）中要比在平方洛伦兹环境模型（双洛伦兹环境模型）中更强健。但对应于远共振条件，得到的结果恰恰相反。然而，在强耦合机制下，不管是原子与赝模满足近共振还是远共振条件，原子的量子discord在平方洛伦兹环境模型（双洛伦兹环境模型）中都比在单洛伦兹环境模型（光子禁带模型）中表现的更强健。对这两种不同的机制，我们分别从环境的谱密度函数和非马尔科夫性出发给出了合理的解释。研究发现：在弱耦合机制中，量子关联单调衰减的速度主要取决于各种环境模型的谱密度函数；而在强耦合机制下，系统量子关联动力学主要依赖于环境模型的非马尔科夫性。
3.利用弱测量与量子反转测量对系统量子态的保护作用，我们分别研究了两初始纠缠比特在共同光子禁带以及各自独立光子禁带下的环境模型，并提出了一个有效的机制来提升两比特发生纠缠俘获时的纠缠量。即在两比特进入退相干信道前后，分别对它们选择合适的弱测量和量子反转操作。在共同光子禁带模型中，我们着重分析了最优纠缠俘获及其成功几率与弱测量强度的关系。并且指出对比特做弱测量操作可以抑制光子禁带模型中的纠缠突然死亡现象。在独立光子禁带模型中，主要研究了最优纠缠俘获与前弱测量强度以及系统初始纠缠度的依赖关系。
4.研究了由初始经典混合分离态产生系统量子纠缠和量子discord的物理机制。讨论两个初始处于分离混合态的二能级原子与其共同热库相耦合的物理模型，利用赝模理论的方法，在考虑了两原子间偶极相互作用以及原子与热库的相对耦合强度的前提下，研究发现：两原子会发生纠缠的突然产生现象，甚至会产生稳定的量子关联。另外，通过改变两原子的初始条件，原子间的偶极相互作用参数以及原子与热库的相对耦合强度可以操控两原子纠缠突然产生的发生时间以及所产生的稳定量子关联值的大小。
Quantum information science is the combination of quantum mechanics and informationscience. As a new cross subject, the birth and development of quantum information science is offar-reaching significance in science and technology. Compared with classical informationprocessing, the quantum information processing has great advantages. For example, a quantumcomputer can exponentially speedup the algorithms that cannot be performed with a classicalcomputer, and quantum communication enables us to transfer information in a definitely safemanner. As everyone knows, the necessary requirement for performing quantum informationprocessing is that the system is quantum-correlated. Quantum entanglement is an importantresource in quantum information science, and its development determines whether the quantuminformation science has a widen application foreground. However the inevitable interactionbetween the quantum system and environment will eventually destroy the quantum entanglementof the whole quantum system. This local decoherence is the main obstacle in the realization ofthe quantum computer. So the study of entanglement dynamics of open quantum system undervarious environmental models is necessary and meaningful. The main results of this thesis are asfollows:
1. Considering three different environmental models (i.e., single reservoir model, commonreservoir model and independent reservoir model), we investigate the evolutional characters ofthe entangled system initially structured in Bell-like states by utilizing the pseudomode method.Through comparing the entanglement decays under these three different environmental models,we acquire an optimal environment model in which the initial entanglement would be preservedmuch better. In particular, when the spectral density of reservoir is satisfied as an ideal photonicband gap, we find that the initial entanglement between two qubits via these three differentdecoherence models all would display entanglement trapping. By comparing the roles ofdifferent decoherence models on the entanglement trapping for the same initial entangled state,we examine the conditions in which the larger entanglement trapping can be achieved.
2. We investigate the roles of different environmental models on quantum correlation decayof a two-qubit composite system interacting with two independent environments. The mostcommon environmental models (the single-Lorentzian model, the squared-Lorentzian model, thetwo-Lorentzian model and band gap model) are analyzed. We find that, for the weak couplingregime, the two-qubit quantum discord in the single-Lorentzian (band gap) environment is morerobust than in the squared-Lorentzian (two-Lorentzian) environment under the resonant and nearresonant conditions, while for the far off-resonant condition the two-qubit quantum discord in thesingle-Lorentzian (band gap) environment decreases much faster than in the squared-Lorentzian (two-Lorentzian) environment. However, by considering the strong coupling regime we find thatthe two-qubit quantum discord is more robust in the squared-Lorentzian (two-Lorentzian)environment than in the single-Lorentzian (band gap) environment, either under the nearresonant or the far off-resonant condition. We give out the reasonable explanations from spectraldensity function and environmental non-Markovian effect for the different results of these tworegimes. We note that, for the weak coupling regime, the monotonic decay speed of the quantumcorrelation is mainly determined by the spectral density functions of these different environments.While, by considering the strong coupling regime, contrary to what is stated in the weakcoupling regime, we find that the dynamics of quantum correlation primarily depends on thenon-Markovianity of the environmental models.
3. We propose a scheme to enhance trapping of entanglement of two qubits, in thecommon environment of a photonic band gap and two independent environments of photonicband gaps respectively, by weak measurement and quantum measurement reversal. Firstly,before the qubits undergoing decoherence, we perform a weak measurement on each qubitsrespectively. While after the system undergoing the evolution process, a suitablepost-measurement (weak measurement or quantum measurement reversal) on these two qubitsare performed. In the common photonic band gap model, we study the relation among theoptimal entanglement trapping, the corresponding success probability and weak measurementstrength. Moreover, we indicate that the prior weak measurement can be used to prevententanglement sudden death (ESD) in the photonic band gap, but the post measurements alonecannot circumvent ESD-causing. In the independent photonic band gap models, we mainlyinvestigate the relation among the optimal entanglement trapping, the pre-measurement strengthand the system initial states.
4. We study the physical mechanism on generating the quantum entanglement and quantumdiscord via the initial classical-mixed states. Using the pseudomode method, we theoreticallyanalyze a realistic situation in which two two-level dipole-dipole interacting atoms coupled witha common structured reservoir with different coupling strengths. By considering certain classesof initial separable-mixed states, we find that the atomic entanglement sudden birth takes placeand the generation of stationary quantum correlations occur. In addition, the occurrence time ofentanglement sudden birth and the stationary values of quantum correlations are related to theinitial conditions of states, the dipole-dipole interaction and the relative coupling strength.
1.详细讨论了不同环境模型中Bell型纠缠态系统的纠缠动力学。通过建立三种不同的环境模型（单一热库模型、共同热库模型和独立热库模型），利用赝模理论的方法，分析比较了初始处于Bell型纠缠态系统的纠缠动力学特性，给出了系统纠缠保持较优的环境模型。特别地，当热库谱密度为光子禁带时，选择合适的参数使光子禁带为理想带隙，研究发现在上述三种不同的比特-环境退相干信道中，都会发生两比特纠缠俘获现象。对比不同退相干信道模型对比特间纠缠俘获现象的影响，我们给出获得较大纠缠俘获的条件。
2.主要研究了不同的退相干环境对原子系统量子关联动力学的影响。考虑两个初始具有量子关联的原子分别与两个独立的局域环境相互作用的物理模型。主要对比研究了四种典型的环境模型：单洛伦兹环境模型，平方洛伦兹环境模型，双洛伦兹环境模型和光子禁带模型。研究发现，在弱耦合机制下，当原子与赝模满足共振或者近共振条件时，原子的量子discord在单洛伦兹环境模型（光子禁带模型）中要比在平方洛伦兹环境模型（双洛伦兹环境模型）中更强健。但对应于远共振条件，得到的结果恰恰相反。然而，在强耦合机制下，不管是原子与赝模满足近共振还是远共振条件，原子的量子discord在平方洛伦兹环境模型（双洛伦兹环境模型）中都比在单洛伦兹环境模型（光子禁带模型）中表现的更强健。对这两种不同的机制，我们分别从环境的谱密度函数和非马尔科夫性出发给出了合理的解释。研究发现：在弱耦合机制中，量子关联单调衰减的速度主要取决于各种环境模型的谱密度函数；而在强耦合机制下，系统量子关联动力学主要依赖于环境模型的非马尔科夫性。
3.利用弱测量与量子反转测量对系统量子态的保护作用，我们分别研究了两初始纠缠比特在共同光子禁带以及各自独立光子禁带下的环境模型，并提出了一个有效的机制来提升两比特发生纠缠俘获时的纠缠量。即在两比特进入退相干信道前后，分别对它们选择合适的弱测量和量子反转操作。在共同光子禁带模型中，我们着重分析了最优纠缠俘获及其成功几率与弱测量强度的关系。并且指出对比特做弱测量操作可以抑制光子禁带模型中的纠缠突然死亡现象。在独立光子禁带模型中，主要研究了最优纠缠俘获与前弱测量强度以及系统初始纠缠度的依赖关系。
4.研究了由初始经典混合分离态产生系统量子纠缠和量子discord的物理机制。讨论两个初始处于分离混合态的二能级原子与其共同热库相耦合的物理模型，利用赝模理论的方法，在考虑了两原子间偶极相互作用以及原子与热库的相对耦合强度的前提下，研究发现：两原子会发生纠缠的突然产生现象，甚至会产生稳定的量子关联。另外，通过改变两原子的初始条件，原子间的偶极相互作用参数以及原子与热库的相对耦合强度可以操控两原子纠缠突然产生的发生时间以及所产生的稳定量子关联值的大小。
Quantum information science is the combination of quantum mechanics and informationscience. As a new cross subject, the birth and development of quantum information science is offar-reaching significance in science and technology. Compared with classical informationprocessing, the quantum information processing has great advantages. For example, a quantumcomputer can exponentially speedup the algorithms that cannot be performed with a classicalcomputer, and quantum communication enables us to transfer information in a definitely safemanner. As everyone knows, the necessary requirement for performing quantum informationprocessing is that the system is quantum-correlated. Quantum entanglement is an importantresource in quantum information science, and its development determines whether the quantuminformation science has a widen application foreground. However the inevitable interactionbetween the quantum system and environment will eventually destroy the quantum entanglementof the whole quantum system. This local decoherence is the main obstacle in the realization ofthe quantum computer. So the study of entanglement dynamics of open quantum system undervarious environmental models is necessary and meaningful. The main results of this thesis are asfollows:
1. Considering three different environmental models (i.e., single reservoir model, commonreservoir model and independent reservoir model), we investigate the evolutional characters ofthe entangled system initially structured in Bell-like states by utilizing the pseudomode method.Through comparing the entanglement decays under these three different environmental models,we acquire an optimal environment model in which the initial entanglement would be preservedmuch better. In particular, when the spectral density of reservoir is satisfied as an ideal photonicband gap, we find that the initial entanglement between two qubits via these three differentdecoherence models all would display entanglement trapping. By comparing the roles ofdifferent decoherence models on the entanglement trapping for the same initial entangled state,we examine the conditions in which the larger entanglement trapping can be achieved.
2. We investigate the roles of different environmental models on quantum correlation decayof a two-qubit composite system interacting with two independent environments. The mostcommon environmental models (the single-Lorentzian model, the squared-Lorentzian model, thetwo-Lorentzian model and band gap model) are analyzed. We find that, for the weak couplingregime, the two-qubit quantum discord in the single-Lorentzian (band gap) environment is morerobust than in the squared-Lorentzian (two-Lorentzian) environment under the resonant and nearresonant conditions, while for the far off-resonant condition the two-qubit quantum discord in thesingle-Lorentzian (band gap) environment decreases much faster than in the squared-Lorentzian (two-Lorentzian) environment. However, by considering the strong coupling regime we find thatthe two-qubit quantum discord is more robust in the squared-Lorentzian (two-Lorentzian)environment than in the single-Lorentzian (band gap) environment, either under the nearresonant or the far off-resonant condition. We give out the reasonable explanations from spectraldensity function and environmental non-Markovian effect for the different results of these tworegimes. We note that, for the weak coupling regime, the monotonic decay speed of the quantumcorrelation is mainly determined by the spectral density functions of these different environments.While, by considering the strong coupling regime, contrary to what is stated in the weakcoupling regime, we find that the dynamics of quantum correlation primarily depends on thenon-Markovianity of the environmental models.
3. We propose a scheme to enhance trapping of entanglement of two qubits, in thecommon environment of a photonic band gap and two independent environments of photonicband gaps respectively, by weak measurement and quantum measurement reversal. Firstly,before the qubits undergoing decoherence, we perform a weak measurement on each qubitsrespectively. While after the system undergoing the evolution process, a suitablepost-measurement (weak measurement or quantum measurement reversal) on these two qubitsare performed. In the common photonic band gap model, we study the relation among theoptimal entanglement trapping, the corresponding success probability and weak measurementstrength. Moreover, we indicate that the prior weak measurement can be used to prevententanglement sudden death (ESD) in the photonic band gap, but the post measurements alonecannot circumvent ESD-causing. In the independent photonic band gap models, we mainlyinvestigate the relation among the optimal entanglement trapping, the pre-measurement strengthand the system initial states.
4. We study the physical mechanism on generating the quantum entanglement and quantumdiscord via the initial classical-mixed states. Using the pseudomode method, we theoreticallyanalyze a realistic situation in which two two-level dipole-dipole interacting atoms coupled witha common structured reservoir with different coupling strengths. By considering certain classesof initial separable-mixed states, we find that the atomic entanglement sudden birth takes placeand the generation of stationary quantum correlations occur. In addition, the occurrence time ofentanglement sudden birth and the stationary values of quantum correlations are related to theinitial conditions of states, the dipole-dipole interaction and the relative coupling strength.
引文
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