单光子多比特体系在量子信息中的应用研究
摘要
量子力学诞生于20世纪初期,但是这个理论从它诞生开始,就存在着不同的理解和争论。随着科学家之间的争论,人们对量子力学的认识更加深刻和确信。20世纪90年代,量子力学与信息科学的相结合,更是将信息科学的发展带入了一个新天地。量子信息科学主要包括量子通信和量子计算,而量子信息科学的基础则是量子态的制备、变换、传输、存储以及测量。很多系统可以被用来作为研究量子信息科学的平台,常见的有光学体系、核磁共振体系(NMR)、腔动力学体系(Cavity QED)、量子点(Quantum Dot)和原子系综等。光学体系相对于其它体系相对全面,而且光子具有环境消相干小,便于操纵等优点。首先,现代通信的基础便是光纤网络,光子是天然的飞行比特,因而量子通信的研究基本都在光学体系中展开;其次,随着2001年,Knill,Laflamme和Milburn三人在自然杂志发表一篇论文,证明了线性光学方法实现大规模量子计算的可能性,推动了光学体系在量子计算方面的研究。
单光子多比特体系是线性光学方法研究量子信息问题的基本内容之一。其基本思想是,利用光子的各种性质在单个光子上编码两比特或更多比特的信息,用来作为研究量子信息问题的载体。常见编码光子比特的有光子偏振、光子空间动量和光子轨道角动量,而光子空间动量和光子角动量可以用来编码高维体系(qudit)。单光子多比特体系可以用来很好的研究量子态的叠加性质,也是向多体、高维推广的基础。我们在实验上利用单光子多比特体系,研究了量子随机行走算法,量子博弈问题和单比特量子幺正操作完美区分。
Ⅰ、光子轨道角动量和量子随机行走
光子轨道角动量与光场的空间模式有着密切的关系。对于Laguerre-Gaussian(LG)模式光,每个光子携带lh的轨道角动量,其中,为整数,表示轨道角动量量子数,也表示exp(ilφ)螺旋波前的单模光的模式。不同,的轨道角动量构成完备的Hilbert空间,所以可以用来编码qubit或者qudit。我们用全息照相技术,制作用来产生各种模式激光的计算全息片,并将其应用于量子随机行走的实验。
量子随机行走是一种量子算法,与经典随机行走有着完全不同的现象和结果。量子随机行走算法已经在很多体系中实现,包括光学体系。在我们实验中,利用光子的路径编码qubit,光子的轨道角动量编码qudit,实现光子在轨道角动量空间上的随机行走。具体是先将光子制备到路径叠加态,然后根据不同路径,通过计算全息片实现轨道角动量的改变,最后探测光子处于各个轨道角动量态的几率,便得到了量子随机行走的结果。我们巧妙地将光子轨道角动量的高维特性应用于实验,得到了更为漂亮的结果,并且讨论了将量子随机行走向更多步数推广的实验可行性。这些内容将在第二章和第三章中详细讨论。
Ⅱ、量子博弈
量子博弈是运筹学与量子理论结合的产物,是量子信息论的一个重要分支。量子博弈主要分为三类问题:PQ翻硬币问题、“囚徒困境”问题和量子赌博。我们在实验上,利用线性光学方法,实现了量子赌博机,并对结果进行了分析,得出博弈方获得最大收益的最佳方案。实验中,我们使用两块双折射晶体作为偏振分束器,解决了Mach-Zehnder干涉稳定性的问题,获得了长时间的干涉稳定,使得实验结果更具说服力。第四章我们将详细介绍量子博弈论的基本问题和实验实现量子赌博机的具体情况。
Ⅲ、量子幺正操作的完美区分
量子态的区分是量子信息中的基本问题,科学家在研究量子态局域操作可区分性方面做出了大量的工作,取得了很大的进展。量子幺正操作的区分与量子态区分类似,有着重要的意义,但是又不同于量子态的区分。理论上已经证明,任意两个不同的么正操作U和V,不论它们是否正交(U+V=0),我们总可以通过并行运行该操作有限次的方法或者串行加入辅助幺正操作的方法将它们完美区分。第五章我们将详细介绍量子幺正操作完美区分的两种方案——并行方案和串行方案,并说明我们在实验上如何利用这两种方案,成功地实现了单比特幺正操作的完美区分。最后通过实验结果,讨论了两种方案的优缺点和实验扩展问题。
Quantum mechanics was born in the beginning of the twentieth century,and there were different understandings and debates on this theory through the century. But with the arguments between the scientists,it is clear that the quantum mechanics is a powerful theory in many fields.With the combining of information science and quantum mechanics in ninety years of twentieth century,quantum information science attracts much attention.Quantum information science mainly includes quantum communication and quantum computation.The process of preparation,operation, transmission,storage and measurement quantum state is the fundamental question of quantum information.There are several systems can be used to study the quantum information process,such as linear optics,NMR system,cavity QED,quantum dot, atom system et al.Linear optical system is a good candidate for implementing quantum information process for two reasons.First,the modem communication is based on fiber net,and photons are natural flying bit.So the research of quantum communication is most in the optics system.Second,Knill,Laflamme,and Milbum show that probabilistic two-qubit operations implemented in linear optical circuits with ancilla photons can be used to build a scalable quantum computer.Their work has stimulated much attention on the experimental realization of linear optics quantum computation protocols.
Single-photon few-qubit system is one of the basic linear optics system on quantum information research.The basic idea of single-photon few-qubit system is to encode two or more qubits on a photon by using different characters of photon. Usually,the quantum bit(qubit)can be encoded by polarization,space momentum and orbital angular momentum of photons.Especially,the space momentum and the orbital angular momentum(OAM)of photons can be used to encode high dimensional system(qudit).Single-photon few-qubit system can be used to study the superposition of quantum states,and can be easily extend to many-body or high dimensional systems.We experimentally implemented quantum random walk,quantum gambling machine and perfect discrimination of unitary operations by using single-photon few-qubit system.
1.Orbital angular momentum of photons and quantum random walk
Orbital angular momentum of photons has the relationship with the mode of light. As we know,light beams can carry OAM associated with helicity of their phase fronts, described by a phase term exp(il(?)),carries an OAM of lh per photon,where l can take any integer value.The OAM can make up an infinite dimensional Hilbert space,so it can be used to encode qubit or qudit.Orbital angular momentum of photons can be generated by computer generated holograms which are used in our experiment of quantum random walk.
Quantum random walk is a kind of quantum algorithm,and it is quiet different form classical random walk.Numerous schemes of quantum random walk have been proposed using many kinds of system,including linear optics system.We encode space momentum of photon as a qubit and OAM of photon as a qudit,experimentally study the quantum random walk on the one-dimensional OAM space.We initialize the photons on a superposition of different routes,then change their OAM by using computer generated holograms due to different route.At last,we detect the probabilities of photons on each OAM state,which are also the results of quantum random walk.Because the photons "random walk" on the OAM space,the experimental setup is much simpler and easy to adjust.These contents will be discussed in the chapter two and chapter three.
2.Quantum game
Quantum game is a new region combined with operational research and quantum theory.It is an important embranchment of quantum information.Quantum game contains three main questions:PQ penny flipover,prisoner's dilemma and quantum gambling.We experimentally realize the quantum gambling machine by using optical method,and discuss the best strategy of the participator to maximize their gains.We use two pieces of birefringent material calcites as polarizing beam splitters,which make the Mach-Zehnder interferometer inherently stable,and get the convictive results of the quantum gambling.We will introduce some quantum game theory and our experimental setup in the chapter four.
3.Perfect discrimination of unitary operations
Distinguishable of quantum states is an fundamental question of quantum information,and a lot of works have been done on it.Similar to discrimination of quantum states,discrimination of quantum operation is also very important.But there are some differences between states and operation discrimination.It is shown that two unitary operations U and V can be perfectly discriminated by using parallel scheme or sequential scheme with finite number copies of unknown operation,no matter U and V are orthogonal or not.We will detailed introduce the two schemes of perfect discrimination of two unitary operation and our experiment based on these two schemes.The complexity and resource consumed are analyzed and compared with some other schemes of discrimination of unitary operations.
单光子多比特体系是线性光学方法研究量子信息问题的基本内容之一。其基本思想是,利用光子的各种性质在单个光子上编码两比特或更多比特的信息,用来作为研究量子信息问题的载体。常见编码光子比特的有光子偏振、光子空间动量和光子轨道角动量,而光子空间动量和光子角动量可以用来编码高维体系(qudit)。单光子多比特体系可以用来很好的研究量子态的叠加性质,也是向多体、高维推广的基础。我们在实验上利用单光子多比特体系,研究了量子随机行走算法,量子博弈问题和单比特量子幺正操作完美区分。
Ⅰ、光子轨道角动量和量子随机行走
光子轨道角动量与光场的空间模式有着密切的关系。对于Laguerre-Gaussian(LG)模式光,每个光子携带lh的轨道角动量,其中,为整数,表示轨道角动量量子数,也表示exp(ilφ)螺旋波前的单模光的模式。不同,的轨道角动量构成完备的Hilbert空间,所以可以用来编码qubit或者qudit。我们用全息照相技术,制作用来产生各种模式激光的计算全息片,并将其应用于量子随机行走的实验。
量子随机行走是一种量子算法,与经典随机行走有着完全不同的现象和结果。量子随机行走算法已经在很多体系中实现,包括光学体系。在我们实验中,利用光子的路径编码qubit,光子的轨道角动量编码qudit,实现光子在轨道角动量空间上的随机行走。具体是先将光子制备到路径叠加态,然后根据不同路径,通过计算全息片实现轨道角动量的改变,最后探测光子处于各个轨道角动量态的几率,便得到了量子随机行走的结果。我们巧妙地将光子轨道角动量的高维特性应用于实验,得到了更为漂亮的结果,并且讨论了将量子随机行走向更多步数推广的实验可行性。这些内容将在第二章和第三章中详细讨论。
Ⅱ、量子博弈
量子博弈是运筹学与量子理论结合的产物,是量子信息论的一个重要分支。量子博弈主要分为三类问题:PQ翻硬币问题、“囚徒困境”问题和量子赌博。我们在实验上,利用线性光学方法,实现了量子赌博机,并对结果进行了分析,得出博弈方获得最大收益的最佳方案。实验中,我们使用两块双折射晶体作为偏振分束器,解决了Mach-Zehnder干涉稳定性的问题,获得了长时间的干涉稳定,使得实验结果更具说服力。第四章我们将详细介绍量子博弈论的基本问题和实验实现量子赌博机的具体情况。
Ⅲ、量子幺正操作的完美区分
量子态的区分是量子信息中的基本问题,科学家在研究量子态局域操作可区分性方面做出了大量的工作,取得了很大的进展。量子幺正操作的区分与量子态区分类似,有着重要的意义,但是又不同于量子态的区分。理论上已经证明,任意两个不同的么正操作U和V,不论它们是否正交(U+V=0),我们总可以通过并行运行该操作有限次的方法或者串行加入辅助幺正操作的方法将它们完美区分。第五章我们将详细介绍量子幺正操作完美区分的两种方案——并行方案和串行方案,并说明我们在实验上如何利用这两种方案,成功地实现了单比特幺正操作的完美区分。最后通过实验结果,讨论了两种方案的优缺点和实验扩展问题。
Quantum mechanics was born in the beginning of the twentieth century,and there were different understandings and debates on this theory through the century. But with the arguments between the scientists,it is clear that the quantum mechanics is a powerful theory in many fields.With the combining of information science and quantum mechanics in ninety years of twentieth century,quantum information science attracts much attention.Quantum information science mainly includes quantum communication and quantum computation.The process of preparation,operation, transmission,storage and measurement quantum state is the fundamental question of quantum information.There are several systems can be used to study the quantum information process,such as linear optics,NMR system,cavity QED,quantum dot, atom system et al.Linear optical system is a good candidate for implementing quantum information process for two reasons.First,the modem communication is based on fiber net,and photons are natural flying bit.So the research of quantum communication is most in the optics system.Second,Knill,Laflamme,and Milbum show that probabilistic two-qubit operations implemented in linear optical circuits with ancilla photons can be used to build a scalable quantum computer.Their work has stimulated much attention on the experimental realization of linear optics quantum computation protocols.
Single-photon few-qubit system is one of the basic linear optics system on quantum information research.The basic idea of single-photon few-qubit system is to encode two or more qubits on a photon by using different characters of photon. Usually,the quantum bit(qubit)can be encoded by polarization,space momentum and orbital angular momentum of photons.Especially,the space momentum and the orbital angular momentum(OAM)of photons can be used to encode high dimensional system(qudit).Single-photon few-qubit system can be used to study the superposition of quantum states,and can be easily extend to many-body or high dimensional systems.We experimentally implemented quantum random walk,quantum gambling machine and perfect discrimination of unitary operations by using single-photon few-qubit system.
1.Orbital angular momentum of photons and quantum random walk
Orbital angular momentum of photons has the relationship with the mode of light. As we know,light beams can carry OAM associated with helicity of their phase fronts, described by a phase term exp(il(?)),carries an OAM of lh per photon,where l can take any integer value.The OAM can make up an infinite dimensional Hilbert space,so it can be used to encode qubit or qudit.Orbital angular momentum of photons can be generated by computer generated holograms which are used in our experiment of quantum random walk.
Quantum random walk is a kind of quantum algorithm,and it is quiet different form classical random walk.Numerous schemes of quantum random walk have been proposed using many kinds of system,including linear optics system.We encode space momentum of photon as a qubit and OAM of photon as a qudit,experimentally study the quantum random walk on the one-dimensional OAM space.We initialize the photons on a superposition of different routes,then change their OAM by using computer generated holograms due to different route.At last,we detect the probabilities of photons on each OAM state,which are also the results of quantum random walk.Because the photons "random walk" on the OAM space,the experimental setup is much simpler and easy to adjust.These contents will be discussed in the chapter two and chapter three.
2.Quantum game
Quantum game is a new region combined with operational research and quantum theory.It is an important embranchment of quantum information.Quantum game contains three main questions:PQ penny flipover,prisoner's dilemma and quantum gambling.We experimentally realize the quantum gambling machine by using optical method,and discuss the best strategy of the participator to maximize their gains.We use two pieces of birefringent material calcites as polarizing beam splitters,which make the Mach-Zehnder interferometer inherently stable,and get the convictive results of the quantum gambling.We will introduce some quantum game theory and our experimental setup in the chapter four.
3.Perfect discrimination of unitary operations
Distinguishable of quantum states is an fundamental question of quantum information,and a lot of works have been done on it.Similar to discrimination of quantum states,discrimination of quantum operation is also very important.But there are some differences between states and operation discrimination.It is shown that two unitary operations U and V can be perfectly discriminated by using parallel scheme or sequential scheme with finite number copies of unknown operation,no matter U and V are orthogonal or not.We will detailed introduce the two schemes of perfect discrimination of two unitary operation and our experiment based on these two schemes.The complexity and resource consumed are analyzed and compared with some other schemes of discrimination of unitary operations.
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