论文标题
一维量子步行的历史状态
History states of one-dimensional quantum walks
论文作者
论文摘要
我们分析了历史状态形式主义在量子行走中的应用。形式主义允许人们描述整个过程中的整个量子历史状态，这可以从永恒的特征值方程中得出。它自然会导致步行的系统时间纠缠的概念，这可以被视为衡量步行中访问的正交状态的量度。然后，我们专注于一维离散量子步行，在此表明，这种纠缠独立于对真正的Hadamard型硬币运算符的初始旋转方向和具有确定位置平价的真实初始状态（在标准基础上）。此外，在最初局部粒子的情况下，它可以通过产生整个历史状态的单一全局运算符的纠缠来识别，该状态与其纠缠能力相关，可以进行分析评估。此外，还可以通过扩展时钟来描述自旋子系统的演变。也得出了其平均纠缠（在所有初始状态）与生成此状态的操作员之间的连接。还提供了用于生成量子步行历史状态的量子电路。
We analyze the application of the history state formalism to quantum walks. The formalism allows one to describe the whole walk through a pure quantum history state, which can be derived from a timeless eigenvalue equation. It naturally leads to the notion of system-time entanglement of the walk, which can be considered as a measure of the number of orthogonal states visited in the walk. We then focus on one-dimensional discrete quantum walks, where it is shown that such entanglement is independent of the initial spin orientation for real Hadamard-type coin operators and real initial states (in the standard basis) with definite site parity. Moreover, in the case of an initially localized particle it can be identified with the entanglement of the unitary global operator that generates the whole history state, which is related to its entangling power and can be analytically evaluated. Besides, it is shown that the evolution of the spin subsystem can also be described through a spin history state with an extended clock. A connection between its average entanglement (over all initial states) and that of the operator generating this state is also derived. A quantum circuit for generating the quantum walk history state is provided as well.
