双光子态操控及应用的实验研究
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摘要
量子信息学就是研究用量子态来编码信息,利用其特有的相干叠加、纠缠等性质进行信息的存储、传输和处理的学科。
纠缠(量子关联)是量子物理的核心内容之一,人们以纠缠为基础构造了各种新颖的信息处理方式,如:量子密码术、量子隐形传态、量子超密编码、量子计算等。作为量子信息的关键信息资源,纠缠的描述、制备、操控及其应用一直是量子信息学理论和实验研究中相当活跃的领域。
光子系统作为纠缠的物理载体,在量子信息学的实验研究中一直有其独特的优势。无论是量子密钥分配、量子隐形传态等新型量子信息技术还是量子力学的非局域性检验等基本问题的实验研究都是首先在光子系统中完成的。正因为如此,本论文将光子纠缠态的操控及应用的实验研究作为主要研究内容。
另一方面,量子信息研究中涉及到的关联并不总是纯粹的量子关联(纠缠),而往往是以混合关联的形式出现的,其中既包含了量子关联也包含了经典关联。本文的最后一章中我们进行了与经典关联有关的实验研究。
本文的主要工作如下:
1.设计了能够确定性实现单光子偏振态上任意正算子值测量(positiveoperator-valued measures,简记为POVM)的实验方案,搭建了完全由线性光学元件构成的实验装置。使用上述装置,在实验上首次实现了两体纯态纠缠的非平凡确定性转换。我们设计的POVM测量实现方案比前人的理论方案大大简化,能够方便的在目前实验技术水平下实现,为后续实验提供了很好的工具。在纠缠转换实验中,用POVM测量实现装置确定性执行所需的双输出POVM测量,实现了一类满足Nielsen定理的确定性纠缠转换,纠缠转换所得的双光子偏振纠缠态的平均保真度达到0.96。该实验装置原则上可以完成任意双光子纯态纠缠之间的转换,同时转换效率可以达到最优。
2.提出了实现任意单光子偏振态远程制备的实验方案,并进行了实验验证。方案中远程制备的平均效率比前人的方案更高,成功制备单量子位纯态或混合态平均消耗√2个比特的经典信息,是目前各种实验实现中最低的。实验中得到的18个量子态(包括纯态和混合态)的保真度均高于0.99,平均保真度为0.9956。
3.提出了任意单光子偏振纯态的确定性远程制备的实验方案,进行了原理性的实验验证;应用通过纠缠转换实现量子态远程制备的思想,提出了首个能够实现任意单光子偏振态(包括纯态和混合态)确定性远程制备的实验方案,并进行了实验验证。在前一个方案中,将所需制备的纯态编码在单光子的空间模式上,任意纯态的远程制备效率可达100%;一般混合态的远程制备效率为50%。在后一个方案中,借助确定性的POVM测量实现装置,能够实现任意单光子偏振纯态的确定性远程制备;将POVM测量与控制消相干相结合,能够实现任意单光子偏振混合态的确定性远程制备。我们对方案进行了实验验证,首次在实验上实现了任意单量子位纯态和混合态的确定性远程制备。实验中制备了12个纯态和6个混合态,所有量子态的保真度均高于0.99,平均保真度为0.9947。
4.提出了利用自发参量下转换过程结合控制消相干制备双光子偏振经典关联态的方案,实验制备的经典关联态的保真度达0.9915。利用制备出的经典关联态,使用双光子之间的经典关联而非纠缠,实现了任意单光子偏振态的量子态远程制备,实验中制备的所有量子态保真度均高于0.99。
Exploring the rich variety of capabilities in information processing allowed by thenon-classical properties of quantum states (e.g. quantum superposition and quantum entanglement)is the subject of quantum information technology, which has become one ofthe most popular interdisciplinary fields.
Entanglement lies at the heart of quantum mechanics. It has become a basic buildingblock for many novel quantum protocols, such as quantum key distribution, teleportation,dense coding and quantum computation. It is always a powerful tool that serves as akey resource for quantum communication and quantum computation. Then description,generation, manipulation and application of entanglement have became a very active fieldin theoretical and experimental quantum information science.
Entangled states of various quantum systems have been investigated. To date, theirbiggest variety was observed in photonic qubit systems which is more feasible than others.So the first experiments of quantum key distribution, quantum teleportation and verificationof quantum nonlocality are realized with photonic qubits. The main part of this dissertationconcerns the experimental manipulation and applications of entangled photonsin quantum information science.
Not all correlations between quantum systems, however, are purely quantum correlations(i.e. entanglement). People also find interests in the exciting subjects of characterizingother attractive types of correlations in quantum states. In general, there are quantumcorrelations, classical correlations and the mixture of them. In the last chapter, we makesome experimental studies about classical correlations.
The main contents of this dissertation are as follows
We propose a scheme which can implement arbitrary positive operator-valued measures(POVM) on single-photon polarization state and is deterministic rather than probabilistic.With more feasibility in practice than former similar schemes, this scheme maybe used as a basic tool of various quantum information protocols in future applications.
We experimentally demonstrate a kind of deterministic entanglement transformationsof bipartite pure states, which is the first experimental realization of non-trivial deterministicentanglement transformations. The average fidelity of all output states is 0.96. The protocol employs two-outcome POVM and can transform two-photon maximally entangledstate to any two-photon entangled pure state deterministically. Moreover, in principlewe can realize any kind of entanglement transformation of two-photon entangled purestates with the optimal theoretical upper bound efficiency.
We experimentally demonstrate a protocol of probabilistic remote state preparationby virtue of entanglement, local operation and forward classical communications. Arbitrarypolarization qubit states can be remotely prepared with this protocol. The averageclassical information cost of successful remote preparation is calculated to be cbitper qubit by integrating this state-dependent cost. To our best knowledge, it is the lowestaverage classical information cost of successful remote preparation in all remote statepreparation experiments. All 18 remotely prepared states are estimated with quantum statetomography system, with average fidelity being 0.9956 and the minimal being over 0.99.
By encoding the desired state into the spatial mode of single-photon, 100% efficiencyis obtained for the remote preparation of arbitrary single-photon pure polarization state.For mixed states, polarization insensitive measurement is introduced and the efficiency is50%. We achieve remote preparation of 13 states with fidelities all above 0.994.
We propose a deterministic remote state preparation scheme for arbitrary photon polarizationqubit states, where entanglement, local operations and classical communicationare used. By consuming one maximally entangled state and two classical bits, an arbitrary(either pure or mixed) qubit state can be prepared deterministically at a remote location.We experimentally demonstrate the scheme by remotely preparing 12 pure states and 6mixed states. The fidelities between the desired and achieved states are all higher than0.99 and have an average of 0.9947. The methods used in our experiment can be generalizedto other situations. The operations on the photon can be utilized to remote controlother matter systems provided that the matter system is maximally entangled with singlephoton.
Classically correlated states are experimentally prepared by introducing controlleddecoherence on the entangled photon pairs and the fidelity is 0.9915. We also proposeseveral ways to experimentally prepare classical correlated states with no entanglementinvolved at all. Then the first remote state preparation with no shared entanglement wasexperimentally demonstrated with classically correlated states. To estimate the performanceof our protocol, 42 qubit states are remotely prepared. The fidelities of all remotely prepared states are higher than 0.99.
纠缠(量子关联)是量子物理的核心内容之一,人们以纠缠为基础构造了各种新颖的信息处理方式,如:量子密码术、量子隐形传态、量子超密编码、量子计算等。作为量子信息的关键信息资源,纠缠的描述、制备、操控及其应用一直是量子信息学理论和实验研究中相当活跃的领域。
光子系统作为纠缠的物理载体,在量子信息学的实验研究中一直有其独特的优势。无论是量子密钥分配、量子隐形传态等新型量子信息技术还是量子力学的非局域性检验等基本问题的实验研究都是首先在光子系统中完成的。正因为如此,本论文将光子纠缠态的操控及应用的实验研究作为主要研究内容。
另一方面,量子信息研究中涉及到的关联并不总是纯粹的量子关联(纠缠),而往往是以混合关联的形式出现的,其中既包含了量子关联也包含了经典关联。本文的最后一章中我们进行了与经典关联有关的实验研究。
本文的主要工作如下:
1.设计了能够确定性实现单光子偏振态上任意正算子值测量(positiveoperator-valued measures,简记为POVM)的实验方案,搭建了完全由线性光学元件构成的实验装置。使用上述装置,在实验上首次实现了两体纯态纠缠的非平凡确定性转换。我们设计的POVM测量实现方案比前人的理论方案大大简化,能够方便的在目前实验技术水平下实现,为后续实验提供了很好的工具。在纠缠转换实验中,用POVM测量实现装置确定性执行所需的双输出POVM测量,实现了一类满足Nielsen定理的确定性纠缠转换,纠缠转换所得的双光子偏振纠缠态的平均保真度达到0.96。该实验装置原则上可以完成任意双光子纯态纠缠之间的转换,同时转换效率可以达到最优。
2.提出了实现任意单光子偏振态远程制备的实验方案,并进行了实验验证。方案中远程制备的平均效率比前人的方案更高,成功制备单量子位纯态或混合态平均消耗√2个比特的经典信息,是目前各种实验实现中最低的。实验中得到的18个量子态(包括纯态和混合态)的保真度均高于0.99,平均保真度为0.9956。
3.提出了任意单光子偏振纯态的确定性远程制备的实验方案,进行了原理性的实验验证;应用通过纠缠转换实现量子态远程制备的思想,提出了首个能够实现任意单光子偏振态(包括纯态和混合态)确定性远程制备的实验方案,并进行了实验验证。在前一个方案中,将所需制备的纯态编码在单光子的空间模式上,任意纯态的远程制备效率可达100%;一般混合态的远程制备效率为50%。在后一个方案中,借助确定性的POVM测量实现装置,能够实现任意单光子偏振纯态的确定性远程制备;将POVM测量与控制消相干相结合,能够实现任意单光子偏振混合态的确定性远程制备。我们对方案进行了实验验证,首次在实验上实现了任意单量子位纯态和混合态的确定性远程制备。实验中制备了12个纯态和6个混合态,所有量子态的保真度均高于0.99,平均保真度为0.9947。
4.提出了利用自发参量下转换过程结合控制消相干制备双光子偏振经典关联态的方案,实验制备的经典关联态的保真度达0.9915。利用制备出的经典关联态,使用双光子之间的经典关联而非纠缠,实现了任意单光子偏振态的量子态远程制备,实验中制备的所有量子态保真度均高于0.99。
Exploring the rich variety of capabilities in information processing allowed by thenon-classical properties of quantum states (e.g. quantum superposition and quantum entanglement)is the subject of quantum information technology, which has become one ofthe most popular interdisciplinary fields.
Entanglement lies at the heart of quantum mechanics. It has become a basic buildingblock for many novel quantum protocols, such as quantum key distribution, teleportation,dense coding and quantum computation. It is always a powerful tool that serves as akey resource for quantum communication and quantum computation. Then description,generation, manipulation and application of entanglement have became a very active fieldin theoretical and experimental quantum information science.
Entangled states of various quantum systems have been investigated. To date, theirbiggest variety was observed in photonic qubit systems which is more feasible than others.So the first experiments of quantum key distribution, quantum teleportation and verificationof quantum nonlocality are realized with photonic qubits. The main part of this dissertationconcerns the experimental manipulation and applications of entangled photonsin quantum information science.
Not all correlations between quantum systems, however, are purely quantum correlations(i.e. entanglement). People also find interests in the exciting subjects of characterizingother attractive types of correlations in quantum states. In general, there are quantumcorrelations, classical correlations and the mixture of them. In the last chapter, we makesome experimental studies about classical correlations.
The main contents of this dissertation are as follows
We propose a scheme which can implement arbitrary positive operator-valued measures(POVM) on single-photon polarization state and is deterministic rather than probabilistic.With more feasibility in practice than former similar schemes, this scheme maybe used as a basic tool of various quantum information protocols in future applications.
We experimentally demonstrate a kind of deterministic entanglement transformationsof bipartite pure states, which is the first experimental realization of non-trivial deterministicentanglement transformations. The average fidelity of all output states is 0.96. The protocol employs two-outcome POVM and can transform two-photon maximally entangledstate to any two-photon entangled pure state deterministically. Moreover, in principlewe can realize any kind of entanglement transformation of two-photon entangled purestates with the optimal theoretical upper bound efficiency.
We experimentally demonstrate a protocol of probabilistic remote state preparationby virtue of entanglement, local operation and forward classical communications. Arbitrarypolarization qubit states can be remotely prepared with this protocol. The averageclassical information cost of successful remote preparation is calculated to be cbitper qubit by integrating this state-dependent cost. To our best knowledge, it is the lowestaverage classical information cost of successful remote preparation in all remote statepreparation experiments. All 18 remotely prepared states are estimated with quantum statetomography system, with average fidelity being 0.9956 and the minimal being over 0.99.
By encoding the desired state into the spatial mode of single-photon, 100% efficiencyis obtained for the remote preparation of arbitrary single-photon pure polarization state.For mixed states, polarization insensitive measurement is introduced and the efficiency is50%. We achieve remote preparation of 13 states with fidelities all above 0.994.
We propose a deterministic remote state preparation scheme for arbitrary photon polarizationqubit states, where entanglement, local operations and classical communicationare used. By consuming one maximally entangled state and two classical bits, an arbitrary(either pure or mixed) qubit state can be prepared deterministically at a remote location.We experimentally demonstrate the scheme by remotely preparing 12 pure states and 6mixed states. The fidelities between the desired and achieved states are all higher than0.99 and have an average of 0.9947. The methods used in our experiment can be generalizedto other situations. The operations on the photon can be utilized to remote controlother matter systems provided that the matter system is maximally entangled with singlephoton.
Classically correlated states are experimentally prepared by introducing controlleddecoherence on the entangled photon pairs and the fidelity is 0.9915. We also proposeseveral ways to experimentally prepare classical correlated states with no entanglementinvolved at all. Then the first remote state preparation with no shared entanglement wasexperimentally demonstrated with classically correlated states. To estimate the performanceof our protocol, 42 qubit states are remotely prepared. The fidelities of all remotely prepared states are higher than 0.99.
引文
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