Analysis of non-locality of quantum mechanics in terms of quantum trajectories and quantum teleportation of continuous variables

1.用玻姆轨道分析位形空间中量子纠缠的非定域性我们分析了位形空间中纠缠的两个粒子的玻姆轨道的非定域关联。我们使用一维波包模型，明确地描述了两粒子纠缠态的时空演化。这种分析证实了赖斯早先用来证明量子力学玻姆理论中的非定域性的几何图解方法。我们进一步讨论了非局部相关性的一个微妙方面，这在赖斯的分析中没有揭示出来。我们还用一维波包模型研究了一个三粒子纠缠态。2.一个位置动量量子态的非相对论含时隐形传态我们构造了一个位置动量未知量子态的含时隐形传态模型。我们对两粒子纠缠态采用高斯型关联函数。有了这个模型，我们分析了一种情况下，在接收器的站点产生的测量后状态的时间演化不能被忽略，接收器是无知的描述时间演化的哈密顿量。我们说明了测量后态的时间演化如何降低量子隐形传态的保真度。我们还举例说明了一种特殊的情况，即双模输入态通过隐形传态转化为单模输入态。此外，我们还讨论了一种最佳情况，在这种情况下，可以同时获得高的隐形传态概率和高的隐形传态保真度。3.相关问题我们研究了各种类型的广义点相互作用，并将它们应用到一种新的量子寄存器模型中。此外，我们还研究了隧穿加速的量子衰变过程、小宽度波包的透射和反射等。

1.Analysis of non-locality of quantum entanglement in configuration space in terms of Bohm trajectoriesWe analyzed non-local correlations in Bohm trajectories of two particles that are entangled in configuration space. We used a one-dimensional wave-packet model that explicitly describes the space-time evolution of a two-particle entangled state. This analysis substantiates the geometrical, schematic approach that was used earlier by Rice to demonstrate non-locality in the Bohm theory of quantum mechanics. We further discussed a subtle aspect of the non-local correlations that was not revealed in Rice's analysis. We also examined a three-particle entangled state with a one-dimensional wave-packet model.2.A non-relativistic time-dependent model for teleportation of a quantum state of position and momentumWe constructed a time-dependent model for teleportation of an unknown quantum state of position and momentum. We used a correlation function of the Gaussian type for the two-particle entangled state. With this model, we analyzed a situation where a time-evolution of a post-measurement state generated at the receiver's site cannot be ignored and the receiver is ignorant of the Hamiltonian that describes the time-evolution. We illustrated how the time-evolution of the post-measurement state deteriorates the fidelity of the quantum teleportation. We also illustrated a special situation in which a two-mode input state is transformed into a one-mode state by teleportation. In addition, we discussed an optimal situation in which a high teleportation probability and a high degree of teleportation fidelity can be achieved.3.Related problemsWe examined generalized point interactions of various types to apply them to a new model of quantum register. In addition, we examined quantum decay process accelerated by tunneling, transmission and reflection of a wave packet with a small width and so on.