腔QED系统中量子关联的理论研究
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摘要
量子信息学是量子力学与信息科学相结合的一门新兴交叉学科,主要包括量子计算、量子通讯和量子密码三个领域。量子信息处理具有经典信息处理无法比拟的优越性,如量子计算可以指数倍的增加经典计算的速度,量子保密通讯可以做到绝对意义上的安全通讯并能发觉窃听者的存在等等。然而实现绝大部分量子信息处理过程的前提条件是系统中存在量子关联。因此量子信息学的研究在一定程度上是对量子系统中量子关联的研究。
量子关联是不仅是量子力学区别于经典力学的基本特征之一,而且在量子信息学中起着至关重要的作用。近年来,作为量子关联的度量,无论是量子纠缠还是量子discord都引起了人们的广泛关注。另一方面要实现量子信息处理过程,寻找合适的量子系统作为“硬件”也是量子信息学的一个主要研究方向。目前人们已经研究了许多量子系统,在这些系统中腔量子电动力学(Quantum electrodynamic， QED)系统由于其成熟的制造工艺与实验技术手段,成为最有潜力实现量子计算的系统之一。因此本文主要研究了在腔量子电动力学系统中量子关联的性质以及测量。全文分为七章,其中第三章到第七章为本人博士期间的主要工作,论文章节具体安排如下：
第一章简要介绍了本文的研究背景,回顾了量子信息学的产生与发展过程,并简单介绍量子关联在量子信息过程中的作用。
第二章介绍了与本文中将要用到的基本知识和概念,其中包括量子比特,密度矩阵,量子纠缠度量,量子关联度量以及腔QED系统。
第三章我们讨论了在一种新型的光学微腔—微芯圆环腔中原子纠缠与腔的散射强度的关系。所谓散射强度是指由于腔的内表面的粗糙度导致的腔内传播方向相反的两个耳语回廊模式腔模的耦合强度。直观上人们认为为了得到更大的纠缠,腔的表面应该尽可能的光滑以减少演化过程中纠缠的损耗。然而我们发现在有些情况下粗糙的腔内表面对原子纠缠起着正面作用,适当的表面粗糙度可以增加原子的纠缠,而且它还可以补偿由腔泄漏和原子自发辐射导致的纠缠损耗。
第四章我们讨论了在腔QED系统中利用噪声环境来产生稳定的量子discord。我们所研究的模型是由传统的Fabry-Perot腔与两个二能级原子组成。我们发现当白噪声仅驱动在腔模或者原子上时,可以产生稳定的非零量子discord,然而当白噪声同时驱动腔模和原子时,原子之间的量子discord将消失。特别地,我们还发现白噪声在稳定的量子discord形成过程起着不同的作用。
第五章我们讨论在两个距离较远的光学腔中实现长距离的原子未知态的量子隐形传态。我们提出的方案是利用被囚禁的原子辐射出的不可分辨的光子的量子统计效应。该方案的成功几率不依赖于待传送的量子态,而且在Lamb-Dicke极限下,不需要光子探测器同时计数。
第六章我们讨论了关于量子discord的直接测量问题。我们提出了一种方案直接测量几何量子discord确切值而不是仅给出上界或者下界。该方案只需要进行反对称子空间的投影测量,相比于目前广泛应用的量子态层析技术该方案更加有效率,因为它需要测量更少的参数。此外,该方案可以在现有的实验技术条件下实现。
第七章我们讨论了对于一些特殊量子态的非破坏测量与识别问题。我们讨论了Werner态的非破坏测量问题,并推广到处于Werner态的量子比特被相距较远的两个参与者共享情况下的非破坏测量。令人感兴趣的是我们的方案对于测量过程引入的耗散效应具有良好的鲁棒性。另外,我们还介绍了一种识别未知Bell对角态的方案,该方案的显著优点是在对探测量子比特进行测量后这个系统会塌缩到与待探测(?) Bell对角态相同的系综上,即该方案是非破坏性的。我们在腔QED系统中讨论了对上述两个方案的具体实现。
最后,我们给出了本文的总结与展望。
Quantum information theory is an interdiscipline between quantum mechanics and infor-mation science, which consists of quantum computation, quantum communication and quan-tum cryptography. The quantum information processing is much more advanced than classi-cal information processing. For example, a quantum computer can exponentially speedup the algorithms that cannot be performed with a classical computer, and quantum communication enables us to transfer information in a definitely safe manner. The necessary requirement for performing quantum information processing is that the system is quantum-correlated. Therefore, studies on quantum information are essentially those on quantum correlations in some sense.
Quantum correlation is not only the feature that distinguishing quantum mechanics from classical mechanics but also plays an essential role in quantum information theory. Recently, as the measures of quantum correlation, both quantum entanglement and quantum discord have attracted considerable attention. On the other hand seeking for a suitable quantum system as the 'hardware' to perform quantum information processing is also an urgent requirement. Among the systems currently under study for quantum information, the cavity quantum electrodynamics (cavity QED) system is believed to be one of the candidates of high potential. As a consequence studies on quantum correlation in cavity QED systems are of great importance and are the main themes of this thesis. The thesis consists of seven chapters in which Chaps.3to7covers the main research work performed during my doctoral study.
In Chap.1, the creation and development of quantum information theory are reviewed and the significance of quantum correlation in quantum information theory is discussed.
In Chap.2, some fundamental concepts used in this thesis, such as qubit, density matrix, measures of quantum entanglement and quantum discord are introduced.
In Chap.3, the positive effects of the scattering strength of a microtoroidal cavity on atomic entanglement evolution are studies. The so-called scattering strength is used to characterize the coupling between two whispering gallery modes caused by the roughness of inner surface of the cavity. Intuitively, in order to obtain a larger entanglement one should make the inner surface of the cavity as smooth as possible. However, we find that the rough surface can play a constructive role. In particular, the rough surface can also compensate for the loss of entanglement during the evolution through cavity leakage and atomic spontaneous emission.
In Chap.4, the creation of quantum discord between two two-level atoms trapped in a Fabry-Perot cavity in a noisy environment is discussed. It is shown that nonzero steady-state quantum discord can be obtained when the white-noise field is separately imposed on atoms and cavity, while the steady-state quantum discord reaches zero if both cavity mode and atoms are driven simultaneously by white-noise fields. In particular, we demonstrate that white-noise field in different cases can play different "constructive roles" in the generation of quantum discord.
In Chap.5. a scheme for long-distance teleportation of an unknown atomic state between two atoms that are trapped in separate optical cavities. In this scheme, the probability of success is independent of the state to be teleported. Moreover, in the Lamb-Dicke limit, the requirement of the simultaneous clicks of the detectors is not necessary.
In Chap.6. the direct measurement of quantum discord is discussed. A scheme for directly measuring the exact value instead of a lower or upper bound of geometric quantum discord is proposed. It only requires the projectors in the all anti-symmetric subspace and is more efficient in contrast to the widely adopted quantum state tomography scheme in the sense that fewer parameters are needed to be measured. Moreover, the present scheme can be easily realized with the current experimental techniques.
In Chap.7, nondestructive detection and identification for a special class of states are discussed. A scheme for nondemolition measurement of a Werner state is discussed and then generalized to the case in which two qubits are separately shared. In addition, a scheme for identifying the Bell diagonal state is discussed in this chapter. The distinct advantage of the present scheme is that the evolved joint quantum state will collapse onto the original Bell diagonal state ensemble after the measurement on the probe qubit. This means the scheme is nondestructive. The experimental realization of both schemes are also discussed in the framework of cavity QED.
Finally, conclusions and prospects are given.
量子关联是不仅是量子力学区别于经典力学的基本特征之一,而且在量子信息学中起着至关重要的作用。近年来,作为量子关联的度量,无论是量子纠缠还是量子discord都引起了人们的广泛关注。另一方面要实现量子信息处理过程,寻找合适的量子系统作为“硬件”也是量子信息学的一个主要研究方向。目前人们已经研究了许多量子系统,在这些系统中腔量子电动力学(Quantum electrodynamic， QED)系统由于其成熟的制造工艺与实验技术手段,成为最有潜力实现量子计算的系统之一。因此本文主要研究了在腔量子电动力学系统中量子关联的性质以及测量。全文分为七章,其中第三章到第七章为本人博士期间的主要工作,论文章节具体安排如下：
第一章简要介绍了本文的研究背景,回顾了量子信息学的产生与发展过程,并简单介绍量子关联在量子信息过程中的作用。
第二章介绍了与本文中将要用到的基本知识和概念,其中包括量子比特,密度矩阵,量子纠缠度量,量子关联度量以及腔QED系统。
第三章我们讨论了在一种新型的光学微腔—微芯圆环腔中原子纠缠与腔的散射强度的关系。所谓散射强度是指由于腔的内表面的粗糙度导致的腔内传播方向相反的两个耳语回廊模式腔模的耦合强度。直观上人们认为为了得到更大的纠缠,腔的表面应该尽可能的光滑以减少演化过程中纠缠的损耗。然而我们发现在有些情况下粗糙的腔内表面对原子纠缠起着正面作用,适当的表面粗糙度可以增加原子的纠缠,而且它还可以补偿由腔泄漏和原子自发辐射导致的纠缠损耗。
第四章我们讨论了在腔QED系统中利用噪声环境来产生稳定的量子discord。我们所研究的模型是由传统的Fabry-Perot腔与两个二能级原子组成。我们发现当白噪声仅驱动在腔模或者原子上时,可以产生稳定的非零量子discord,然而当白噪声同时驱动腔模和原子时,原子之间的量子discord将消失。特别地,我们还发现白噪声在稳定的量子discord形成过程起着不同的作用。
第五章我们讨论在两个距离较远的光学腔中实现长距离的原子未知态的量子隐形传态。我们提出的方案是利用被囚禁的原子辐射出的不可分辨的光子的量子统计效应。该方案的成功几率不依赖于待传送的量子态,而且在Lamb-Dicke极限下,不需要光子探测器同时计数。
第六章我们讨论了关于量子discord的直接测量问题。我们提出了一种方案直接测量几何量子discord确切值而不是仅给出上界或者下界。该方案只需要进行反对称子空间的投影测量,相比于目前广泛应用的量子态层析技术该方案更加有效率,因为它需要测量更少的参数。此外,该方案可以在现有的实验技术条件下实现。
第七章我们讨论了对于一些特殊量子态的非破坏测量与识别问题。我们讨论了Werner态的非破坏测量问题,并推广到处于Werner态的量子比特被相距较远的两个参与者共享情况下的非破坏测量。令人感兴趣的是我们的方案对于测量过程引入的耗散效应具有良好的鲁棒性。另外,我们还介绍了一种识别未知Bell对角态的方案,该方案的显著优点是在对探测量子比特进行测量后这个系统会塌缩到与待探测(?) Bell对角态相同的系综上,即该方案是非破坏性的。我们在腔QED系统中讨论了对上述两个方案的具体实现。
最后,我们给出了本文的总结与展望。
Quantum information theory is an interdiscipline between quantum mechanics and infor-mation science, which consists of quantum computation, quantum communication and quan-tum cryptography. The quantum information processing is much more advanced than classi-cal information processing. For example, a quantum computer can exponentially speedup the algorithms that cannot be performed with a classical computer, and quantum communication enables us to transfer information in a definitely safe manner. The necessary requirement for performing quantum information processing is that the system is quantum-correlated. Therefore, studies on quantum information are essentially those on quantum correlations in some sense.
Quantum correlation is not only the feature that distinguishing quantum mechanics from classical mechanics but also plays an essential role in quantum information theory. Recently, as the measures of quantum correlation, both quantum entanglement and quantum discord have attracted considerable attention. On the other hand seeking for a suitable quantum system as the 'hardware' to perform quantum information processing is also an urgent requirement. Among the systems currently under study for quantum information, the cavity quantum electrodynamics (cavity QED) system is believed to be one of the candidates of high potential. As a consequence studies on quantum correlation in cavity QED systems are of great importance and are the main themes of this thesis. The thesis consists of seven chapters in which Chaps.3to7covers the main research work performed during my doctoral study.
In Chap.1, the creation and development of quantum information theory are reviewed and the significance of quantum correlation in quantum information theory is discussed.
In Chap.2, some fundamental concepts used in this thesis, such as qubit, density matrix, measures of quantum entanglement and quantum discord are introduced.
In Chap.3, the positive effects of the scattering strength of a microtoroidal cavity on atomic entanglement evolution are studies. The so-called scattering strength is used to characterize the coupling between two whispering gallery modes caused by the roughness of inner surface of the cavity. Intuitively, in order to obtain a larger entanglement one should make the inner surface of the cavity as smooth as possible. However, we find that the rough surface can play a constructive role. In particular, the rough surface can also compensate for the loss of entanglement during the evolution through cavity leakage and atomic spontaneous emission.
In Chap.4, the creation of quantum discord between two two-level atoms trapped in a Fabry-Perot cavity in a noisy environment is discussed. It is shown that nonzero steady-state quantum discord can be obtained when the white-noise field is separately imposed on atoms and cavity, while the steady-state quantum discord reaches zero if both cavity mode and atoms are driven simultaneously by white-noise fields. In particular, we demonstrate that white-noise field in different cases can play different "constructive roles" in the generation of quantum discord.
In Chap.5. a scheme for long-distance teleportation of an unknown atomic state between two atoms that are trapped in separate optical cavities. In this scheme, the probability of success is independent of the state to be teleported. Moreover, in the Lamb-Dicke limit, the requirement of the simultaneous clicks of the detectors is not necessary.
In Chap.6. the direct measurement of quantum discord is discussed. A scheme for directly measuring the exact value instead of a lower or upper bound of geometric quantum discord is proposed. It only requires the projectors in the all anti-symmetric subspace and is more efficient in contrast to the widely adopted quantum state tomography scheme in the sense that fewer parameters are needed to be measured. Moreover, the present scheme can be easily realized with the current experimental techniques.
In Chap.7, nondestructive detection and identification for a special class of states are discussed. A scheme for nondemolition measurement of a Werner state is discussed and then generalized to the case in which two qubits are separately shared. In addition, a scheme for identifying the Bell diagonal state is discussed in this chapter. The distinct advantage of the present scheme is that the evolved joint quantum state will collapse onto the original Bell diagonal state ensemble after the measurement on the probe qubit. This means the scheme is nondestructive. The experimental realization of both schemes are also discussed in the framework of cavity QED.
Finally, conclusions and prospects are given.
引文
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