【作者】 张融；

【导师】 朱士群；

【作者基本信息】 苏州大学 ， 光学工程， 2005， 博士

【摘要】 量子理论与信息科学的结合产生了量子信息科学。量子计算机和量子通信成为人们当前的研究热点课题之一。其中,量子计算机的优越性体现在量子并行计算上,从而可以进行超快速计算和模拟量子系统,并能解决经典计算机无法解决的问题。本博士论文着重研究了量子逻辑门在离子阱中的实现、在腔QED 中量子态的制备以及自旋-1/2 系统中量子纠缠态的度量等问题。实验上通过级联的量子逻辑门来构造量子计算机。任意量子门都可以由二比特控制非门(CN 门)和单比特旋转门(R 门)组成。因此,人们致力于研究如何实现CN 门和R 门。我们提出了一种在离子阱中实现CN 门的简单方法。离子的内态作为一个目标量子比特,内部基态|g> 和激发态|e> 分别表示|0> 和|1> ,离子的声子数态|0> 和|1> 作为控制比特。用两束互相垂直的激光同时控制一个被囚禁在直线阱中的离子,调节沿X 方向和Y 方向的耦合系数,选择合适的演化时间,使耦合系数和Lamb-Dicke(LD)系数满足一定的关系,在子空间{|0>| g> ,|0>|e>,|1>|g>,|1>|e}中演化,可以实现CN 门。这种方法的优点是,只需要二能级离子,对LD 系数没有限制,不需要辅助能级数,就可以实现量子逻辑门,从而在实验上更加简便可行。在量子计算中,量子态是信息的载体,量子信息的加工处理是操纵量子态的过程。对多粒子纠缠态的任意操作是实现量子计算的基础。我们提出一种在腔QED中制备多粒子W 态和GHZ 态的方法。制备的方法是,将原子处于|0> 和|1> 的叠加态,腔场处于相干态,通过腔与原子同时相互作用,选择合适的相互作用时间。然后对腔场进行测量,测量得到腔处于不同的态,相应的原子态将塌缩到不同类型的纠缠态,通过证明所制备的态违背Bell 不等式,说明这些态具有非局域性。假定制备的态满足Bell 不等式,计算得到测量预期值。对于四粒子W 态,选择不同的参数得到前后关系式是相互矛盾的。对于四粒子GHZ 态,得出的数学表达式和物理参数的含义矛盾。所以,所制备的态违背Bell 不等式。量子纠缠是量子计算和量子通信的重要资源,利用纠缠态可以实现量子隐形传更多还原

【Abstract】 The development of quantum information is due to the combination of quantum theory and information theory. The investigation of quantum computer and quantum teleportation have been attracted much attention in recent years. One of the advantages of quantum computer is quantum parallel calculation. The quantum computer can perform ultra-fast calculation, simulate quantum system, and solve problems that cannot be solved by classical digital computer. In this paper, the realization of quantum logic gate in trapped ion, the preparation of multi-qubit entanglement state and the measure of mixed entanglement states in spin-1/2 Heisenberg system are discussed. Quantum computer is formed through combination of quantum logic gates. Since any logic gate can be constructed by two-qubit controlled not gates (CN gate) and one qubit rotation gate (R gate), the realization of the CN and R gates has been studied extensively. We have proposed a simple method to realize CN gate in an ion trap system. The internal state of the ion is a target qubit. The internal ground state |g> and excited state |e> can be expressed by |0> and |1> respectively. The phonon state |0> and |1> are used as control bits. Using two laser beams that are perpendicular to each other, the ion in the trap can be controlled. The coupling strengths along x and y axis can be changed. If the evolution time is properly chosen when the Lamb-Dicke (LD) parameter and the coupling coefficient satisfy certain relation, the CN gate can be realized in the subspace {|00> ,|01>,|10>,|11>}. In this scheme, there is no limitation of LD parameter and no auxiliary level required. Only a two-level ion is necessary. It can be easily realized in an experiment. In quantum computation, the quantum state is the carrier of the information. The manipulation of the quantum information is the process of controlling quantum states. The control of multi-particle entanglement state is the basis of quantum computation. We propose a method to prepare multi-particle entanglement W and GHZ states in cavity QED. The scheme is as follows. The atom is in the state of superposition of 0 and 1 . The cavity is in the coherent state. The atom and the cavity interact with each other with proper interaction time. Then the cavity is measured. If the measured cavity is in different states, the corresponding state of the atom collapses to different entanglement state. It is proven that the prepared entanglement state violates the Bell’s inequality. These states have the property of non-locality. If the prepared states satisfy the Bell’s inequality, the measured expectation value is calculated. For four-particle W state, the relation is contradictory when the parameters are different. For four-particle GHZ state, the mathematical expression is in contradiction with the physical parameters. It is obvious that the states violate the Bell’s inequality. The quantum entanglement is an important resource of quantum computation and quantum information. Through entanglement state, the quantum teleportation, quantum coding and quantum computation can be realized. The Bell’s inequality is the criterion of the entanglement state, but it cannot be used to calculate the entanglement quantitatively. Therefore, scientists are seeking methods to measure the entanglement. For two-particle pure and mixed states, the measurement of the entanglement is well developed. The entanglement of multi-particle pure state can also be calculated. However, the entanglement measurement of multi-particle mixed states still needs to be developed. We investigate the thermal entanglement of two and multi particles in two-and three-dimensional Heisenberg models. Through the quantity of concurrence, the entanglement can be calculated analytically. Through the extended theory of n-concurrence, the global entanglement of three-dimensional Heisenberg XY model in the form of tetrahedron and cubic lattices is investigated. It is shown that the concurrence and global entanglement are the functions of the temperature, the coupling strength and the external magnetic field. One can control the concurrence and the global entanglement through changing the parameters of the system.更多还原