论文标题
转导的离散时间量子步行用于量子状态的工程
Steered discrete-time quantum walks for engineering of quantum states
论文作者
论文摘要
我们分析了转向离散时间量子步行的优势和局限性，以生成由量子系统组成的量子量子系统的量子状态。我们证明，即使在量子步骤的最概括的定义下，复合空间中的所有量子状态都可以通过量子步行来访问，从而将复合材料希尔伯特空间的分叉变成“步行可接近的状态”和“步行不可接近的状态”。我们提供了一种算法，用于从易于实现的产品状态生成任何可访问的状态，以最少的步行步骤（所有单位步长大小）。我们进一步开了一个处方，以在任何此类步行访问状态之间建造最小的量子步行。线性光学元件一直是实施基于硬币的量子步行的流行物理系统，在该步行中，复合空间是由光束的旋转和轨道角动量建立的。我们确定在这样的实施中，所有标准化的量子状态都是“可访问的”。此外，可以使用单个Q板和一对均匀波动板将任何通用量子步骤都可以实现到全局相。然后，我们仅使用Q板和波板提供基于量子步行的方案，以实现任意矢量梁。
We analyze the strengths and limitations of steered discrete time quantum walks in generating quantum states of bipartite quantum systems comprising of a qubit coupled to a qudit system. We demonstrate that not all quantum states in the composite space are accessible through quantum walks, even under the most generalized definition of a quantum step, leading to a bifurcation of the composite Hilbert space into "walk-accessible states" and the "walk-inaccessible states". We give an algorithm for generating any walk-accessible state from a simple-to-realize product state, in a minimal number of walk steps, all of unit step size. We further give a prescription towards constructing minimal quantum walks between any pair of such walk-accessible states. Linear optics has been a popular physical system for implementing coin-based quantum walks, where the composite space is built up of spin and orbital angular momenta of light beams. We establish that in such an implementation, all normalized quantum states are "walk-accessible". Furthermore, any generalized quantum step can be implemented upto a global phase using a single q-plate and a pair of homogeneous waveplates. We then give a quantum walk based scheme for realizing arbitrary vector beams, using only q-plates and waveplates.
