论文标题
操作理论中的交流任务
Communication tasks in operational theories
论文作者
论文摘要
我们调查了一个问题，可以在给定的运营理论中完成哪些交流任务。具体的任务是找出哪些通信矩阵具有与给定理论的状态和测量的准备和衡量实现。为了为这个问题设定一般框架，我们在通信矩阵集中开发了超视矩阵的多数化。这种预订使我们能够确定一个通信任务何时比另一个通信任务更难。此外，我们引入了几种单调，可用于比较和表征通信矩阵。我们观察到，单调不仅可以比较通信矩阵，而且它们在给定理论中的最大值也被认为与理论的某些物理特性有关。然后可以将最大值视为“维度”，从而使我们可以将不同的理论相互比较。我们逐一分析引入的单调元素，并演示了几种可实现的通信矩阵的集合如何不同，重点主要是在给定维度的经典和量子理论之间的差异。
We investigate the question which communication tasks can be accomplished within a given operational theory. The concrete task is to find out which communication matrices have a prepare-and-measure implementation with states and measurement from a given theory. To set a general framework for this question we develop the ultraweak matrix majorization in the set of communication matrices. This preorder gives us means to determine when one communication task is more difficult than another. Furthermore, we introduce several monotones which can be used to compare and characterize the communication matrices. We observe that not only do the monotones allow us to compare communication matrices, but also their maximal values in a given theory are seen to relate to some physical properties of the theory. The maximal values can then be thought as `dimensions', allowing us to compare different theories to each other. We analyse the introduced monotones one by one and demonstrate how the set of implementable communication matrices is different in several theories with the focus being mainly on the difference between classical and quantum theories of a given dimension.
