论文标题
量子步行无限期的因果秩序
Quantum Walks with Indefinite Causal Order
论文作者
论文摘要
在所有现有的量子步行模型中，关于先前存在的固定背景因果结构的假设始终是理所当然的。然而，在这项工作中，我们将摆脱这一默认假设，尤其是通过引入无限期的因果秩序抛弃和调查这种现代情况。我们发现，可以使用我们的新模型来准备理想形状和快速的统一分布。首先，我们将展示一个总是对称的瞬时分布出现在不确定的因果秩序量子步行中，然后为推导条件铺平了道路，使人们能够将进化状态解释为其确定的因果秩序对应物的叠加，但总的来说，这是一般禁止的。状态的时间叠加的这种属性可以从两个过程中的方案推广到涉及许多$ \ Mathcal {n} $进程的情况。最后，我们证明了如何从不确定的因果秩序量子步行中出现真正的统一分布。值得注意的是，除了理想的分布形状外，我们的协议还具有另一个强大的优势，即空间扩散的速度完全达到了理论上的限制，与传统情况相比，人们可能会遇到$ 1/\ sqrt {2} $变性的众所周知的问题。
In all existing quantum walk models, the assumption about a pre-existing fixed background causal structure is always made and has been taken for granted. Nevertheless, in this work we will get rid of this tacit assumption especially by introducing indefinite causal order ways of coin tossing and investigate this modern scenario. We find that an ideal-shape and fast-spreading uniform distribution can be prepared with our new model. First we will show how an always-symmetrical instantaneous distribution appears in an indefinite causal order quantum walk, which then paves the way for deriving conditions that enables one to interpret an evolved state as a superposition of its definite causal order counterparts which is however in general prohibited. This property of temporal superposition of states can be generalized from two-process scenarios to cases where arbitrary many $\mathcal{N}$ processes are involved. Finally, we demonstrate how a genuine uniform distribution emerges from an indefinite causal order quantum walk. Remarkably, besides the ideal shape of the distribution, our protocol has another powerful advantage, that is the speed of spatial spreading reaches exactly the theoretical limit in contrast to conventional cases where one may encounter the well-known issue of a $1/\sqrt{2}$ degeneration.
