纠缠态的制备与纯化
摘要
量子信息是二十世纪八十年代发展起来的，由量子力学和信息科学相结合而形成的一门新兴学科。在量子信息学中，纠缠态扮演着极为重要的角色，可以说如果没有量子纠缠现象，就不会有现在所说的量子信息。纠缠态的特殊物理性质，使量子信息具有经典信息所没有的许多新的特征，纠缠态为信息传输和信息处理提供了新的物理资源，是当前迅速发展着的量子信息科学的基础，在量子通信和量子计算方面有着重要应用。纠缠态是量子通信中量子信息传输的通道，对纠缠态的研究包括纠缠态的制备、纠缠源的分配以及纠缠态的操纵等方面。另外，量子系统的消相干是现在量子信息和量子计算实现过程中的瓶颈。故此，本博士论文主要对纠缠态的制备和纠缠态的纯化两个大方面的问题进行了研究，所做的主要工作有：
一、提出基于线性光学方法的离子纠缠态的制备物理方案。该方案的优点在于没有以前方案中的来自不同的离子的散射光子的相对位相问题；探测的光子为入射的光子，所以比探测散射光子容易；不仅可以从直积态中制备最大纠缠态，而且可以从混合纠缠态中制备得到纯的最大纠缠态。
二、提出基于Λ型三能级原子与相干光场之间的大失谐相互作用的多原子纠缠态和多腔场纠缠相干态的制备物理方案。这里的特色在于利用Λ型三能级原子与相干光场之间的大失谐相互作用的特殊性质设计出实现从原子到相干光场、从相干光场到原子、从原子到原子以及从相干光场到相干光场的量子受控非门操作物理方案，并详细分析了其实验可行性。
三、提出实现任意维系统的已知和未知纯的非最大纠缠态的浓缩一般方案，并给出这些方案在腔QED系统和线性光学系统中的物理实现。研究发现，可以利用广义的受控非门操作实现任意维系统未知非最大纠缠态的浓缩；利用基于量子态的区分的纠缠交换可以实现任意维系统已知非最大纠缠态的浓缩。这里我们只需要利用局域纠缠而非远程纠缠便可提高远程纠缠；对于任意维系统己知非最大纠缠态的浓缩，可以仅仅通过引入一个二能级系统作为辅助来实现。
四、提出未知混合纠缠态的纠缠纯化物理方案。包括基于线性光学方法离子混合纠缠态的纠缠纯化物理方案、基于A型三能级原子与相干光场之间的大失谐相互作用的原子混合纠缠态和混合纠缠相干态的纠缠纯化物理方案。基于线性光学方法离子混合纠缠态的纠缠纯化物理方案无需利用原始的纠缠纯化方案中所固有的但在实验中较难实现的控制非操作，这使得该方案的实验可行性大大提高。并且，该方案是我们所知道的迄今为止的第一个适用于离子混合纠缠态的纠缠纯化物理方案。
五、详细分析了基于线性光学方法的离子纠缠态的制备和混合离子纠缠态的纯化物理方案的实验可行性。
六、基于腔QED方法提出一种能够通过一步操作就可以将联合的Bell态测量转化为单个比特测量的直积的未知原子态隐形传态物理方案，并且成功的概率为1.0。同时，这里的腔衰减和热场对方案没有影响，这无疑大大提高了该方案的实验可行性。
Quantum Information is a new subject, which is the combination of QuantumMechanics and Information Science. Because of its potential application inrevolutionizing the methods by which we manipulate information, QuantumInformation has gained more and more attention recently.
Entangled states play a crucial role in Quantum Information. One can say,Quantum Information can not exist without entanglement. Because of itsnon-locality feature, entangled states become very important physical resources inquantum information processing. As the basis of Quantum Information, entangledstates find its significant applications in quantum communication and quantumcomputation. The research on entangled states includes generation of entangledstates, distribution of entangled resources and manipulation of entangled states, etc.It is well known that, decoherence of quantum system is a bottleneck for therealization of quantum information processing and quantum computation. Thus, inthis PhD thesis, we carried out our research work on the generation of entangledstates and the purification of non-maximally entangled states (includingconcentration of pure non-maximally entangle states and purification of mixedentangled states):
1. Generation of ionic entangled states via linear optics. In the scheme, therelative phase problem inherent in the previous schemes has been avoided; Thephoton to be detected is the input photon, which is easier to be dectected than thescattered photon from the ions; The scheme can generate pure maximally entangledstates not only from product initial states but also from the mixed entangled initialstates.
2. Based on the large detuned interaction between aΛ-type three-level atomand a coherent optical field, we propose the scheme for the generation of multi-atomentangled states and multi-cavity entangled states. The unique advantage of this scheme is that it can realize the controlled-not operations, from atoms to coherentfields, from coherent fields to atoms, from one atom to another, and from onecoherent field to another. The feasibility of the current scheme is aso discussed indetail.
3. General implementation of entanglement concentration for non-maximallyentangled states of arbitrary dimension system and its physical implementation. Theresult shows that, entanglement concentration for the unknown non-maximallyentangled states can be realized by generalized controlled-not operations in arbitrarydimension system; the quantum-state-discrimination-based entanglement swappingcan be used to realize the concentration of known non-maximally entangled states.Here, rather than the remote entanglement we use the local entanglement, which canbe prepared in an easier way than the remote entanglement, to enhance the remoteentanglement; Based on generalized measurement, a general method for theconcentration of a known non-maximally entangled state for arbitrary dimensionalsystem is proposed only by introducing a qubit ancilla, which will greatly simplifythe total concentration process.
4. Entangement purification for unknown mixed entangled states. Anentanglement purification scheme for arbitrary unknown mixed entangled ionicstates is proposed by using linear optical elements. The main advantage of thescheme is that the controlled-not operations inherent in the original entanglementpurification scheme are avoided here, which enhances the feasibility of the schemegreatly. As far as we know, it the first physical scheme for the entanglementpurification of mixed ionic entangled states; The entanglement purification formixed entangled coherent states and mixed entangled atomic states have beenproposed by using the large detuned interaction between aΛ-type three-level atomand a coherent optical field.
5. The feasibility of the generation and purification scheme for ionic system vialinear optical elements is discussed in detail. We conclude that the scheme is wellwithin current technology.
6. A teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement in the teleportation process has been converted into theproduct of the single measurements on qubits in a rather easy way, and the successprobability can reach 1.0. In addition, the current scheme is insensitive to the cavitydecay and thermal field, which enhance its experimental feasibility greatly.
一、提出基于线性光学方法的离子纠缠态的制备物理方案。该方案的优点在于没有以前方案中的来自不同的离子的散射光子的相对位相问题；探测的光子为入射的光子，所以比探测散射光子容易；不仅可以从直积态中制备最大纠缠态，而且可以从混合纠缠态中制备得到纯的最大纠缠态。
二、提出基于Λ型三能级原子与相干光场之间的大失谐相互作用的多原子纠缠态和多腔场纠缠相干态的制备物理方案。这里的特色在于利用Λ型三能级原子与相干光场之间的大失谐相互作用的特殊性质设计出实现从原子到相干光场、从相干光场到原子、从原子到原子以及从相干光场到相干光场的量子受控非门操作物理方案，并详细分析了其实验可行性。
三、提出实现任意维系统的已知和未知纯的非最大纠缠态的浓缩一般方案，并给出这些方案在腔QED系统和线性光学系统中的物理实现。研究发现，可以利用广义的受控非门操作实现任意维系统未知非最大纠缠态的浓缩；利用基于量子态的区分的纠缠交换可以实现任意维系统已知非最大纠缠态的浓缩。这里我们只需要利用局域纠缠而非远程纠缠便可提高远程纠缠；对于任意维系统己知非最大纠缠态的浓缩，可以仅仅通过引入一个二能级系统作为辅助来实现。
四、提出未知混合纠缠态的纠缠纯化物理方案。包括基于线性光学方法离子混合纠缠态的纠缠纯化物理方案、基于A型三能级原子与相干光场之间的大失谐相互作用的原子混合纠缠态和混合纠缠相干态的纠缠纯化物理方案。基于线性光学方法离子混合纠缠态的纠缠纯化物理方案无需利用原始的纠缠纯化方案中所固有的但在实验中较难实现的控制非操作，这使得该方案的实验可行性大大提高。并且，该方案是我们所知道的迄今为止的第一个适用于离子混合纠缠态的纠缠纯化物理方案。
五、详细分析了基于线性光学方法的离子纠缠态的制备和混合离子纠缠态的纯化物理方案的实验可行性。
六、基于腔QED方法提出一种能够通过一步操作就可以将联合的Bell态测量转化为单个比特测量的直积的未知原子态隐形传态物理方案，并且成功的概率为1.0。同时，这里的腔衰减和热场对方案没有影响，这无疑大大提高了该方案的实验可行性。
Quantum Information is a new subject, which is the combination of QuantumMechanics and Information Science. Because of its potential application inrevolutionizing the methods by which we manipulate information, QuantumInformation has gained more and more attention recently.
Entangled states play a crucial role in Quantum Information. One can say,Quantum Information can not exist without entanglement. Because of itsnon-locality feature, entangled states become very important physical resources inquantum information processing. As the basis of Quantum Information, entangledstates find its significant applications in quantum communication and quantumcomputation. The research on entangled states includes generation of entangledstates, distribution of entangled resources and manipulation of entangled states, etc.It is well known that, decoherence of quantum system is a bottleneck for therealization of quantum information processing and quantum computation. Thus, inthis PhD thesis, we carried out our research work on the generation of entangledstates and the purification of non-maximally entangled states (includingconcentration of pure non-maximally entangle states and purification of mixedentangled states):
1. Generation of ionic entangled states via linear optics. In the scheme, therelative phase problem inherent in the previous schemes has been avoided; Thephoton to be detected is the input photon, which is easier to be dectected than thescattered photon from the ions; The scheme can generate pure maximally entangledstates not only from product initial states but also from the mixed entangled initialstates.
2. Based on the large detuned interaction between aΛ-type three-level atomand a coherent optical field, we propose the scheme for the generation of multi-atomentangled states and multi-cavity entangled states. The unique advantage of this scheme is that it can realize the controlled-not operations, from atoms to coherentfields, from coherent fields to atoms, from one atom to another, and from onecoherent field to another. The feasibility of the current scheme is aso discussed indetail.
3. General implementation of entanglement concentration for non-maximallyentangled states of arbitrary dimension system and its physical implementation. Theresult shows that, entanglement concentration for the unknown non-maximallyentangled states can be realized by generalized controlled-not operations in arbitrarydimension system; the quantum-state-discrimination-based entanglement swappingcan be used to realize the concentration of known non-maximally entangled states.Here, rather than the remote entanglement we use the local entanglement, which canbe prepared in an easier way than the remote entanglement, to enhance the remoteentanglement; Based on generalized measurement, a general method for theconcentration of a known non-maximally entangled state for arbitrary dimensionalsystem is proposed only by introducing a qubit ancilla, which will greatly simplifythe total concentration process.
4. Entangement purification for unknown mixed entangled states. Anentanglement purification scheme for arbitrary unknown mixed entangled ionicstates is proposed by using linear optical elements. The main advantage of thescheme is that the controlled-not operations inherent in the original entanglementpurification scheme are avoided here, which enhances the feasibility of the schemegreatly. As far as we know, it the first physical scheme for the entanglementpurification of mixed ionic entangled states; The entanglement purification formixed entangled coherent states and mixed entangled atomic states have beenproposed by using the large detuned interaction between aΛ-type three-level atomand a coherent optical field.
5. The feasibility of the generation and purification scheme for ionic system vialinear optical elements is discussed in detail. We conclude that the scheme is wellwithin current technology.
6. A teleportation scheme for unknown atomic states is proposed in cavity QED. The Bell state measurement in the teleportation process has been converted into theproduct of the single measurements on qubits in a rather easy way, and the successprobability can reach 1.0. In addition, the current scheme is insensitive to the cavitydecay and thermal field, which enhance its experimental feasibility greatly.
引文
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