有序线性空间和范畴作为量子和经典理论信息处理特征化的框架
Ordered linear spaces and categories as frameworks for information-processing characterizations of quantum and classical theory
摘要：
我们回顾了我们最近的一些结果（与合作者）在一个有序的线性空间框架的概率理论的信息处理。这些包括许多“固有量子”现象实际上是非经典理论的普遍特征，量子或其他。作为一个例子，在这样一个理论中的一组状态是可广播的，当且仅当它包含在一个顶点是可克隆的单纯形中，因此可以通过一个单一的测量来区分。作为另一个例子，在这个框架中可以获得的关于系统的信息，而不会对系统状态造成干扰，必须是固有的经典。我们还回顾了在这个框架中的隐形传态协议的结果，以及在这个框架中，任何没有纠缠的非经典理论都允许指数安全的比特承诺的事实。最后，我们勾勒出一些方式来制定我们的框架的范畴，并在这方面考虑我们的工作的关系，阿布拉姆斯基，Coecke，Selinger，贝兹和其他人的信息处理和其他方面的理论制定的范畴。
英文摘要：
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite general characteristics of non-classical theories, quantum or otherwise. As an example, a set of states in such a theory is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. As another example, information that can be obtained about a system in this framework without causing disturbance to the system state, must be inherently classical. We also review results on teleportation protocols in the framework, and the fact that any non-classical theory without entanglement allows exponentially secure bit commitment in this framework. Finally, we sketch some ways of formulating our framework in terms of categories, and in this light consider the relation of our work to that of Abramsky, Coecke, Selinger, Baez and others on information processing and other aspects of theories formulated categorically.
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