论文标题
准备不确定性意味着一类普遍概率理论的测量不确定性
Preparation Uncertainty Implies Measurement Uncertainty in a Class of Generalized Probabilistic Theories
论文作者
论文摘要
在量子理论中，以一对非交通性观察结果而闻名，没有哪个状态同时获得确定的值，并且没有对它们的关节测量。它们被称为制备不确定性和测量不确定性，研究表明，它们不是独立的，而是以定量的方式相互关联。这项研究旨在揭示与量子量相似的关系是否也存在于广义概率理论（GPT）中。特别是，考虑到某种类别的GPT可以以传递性和自以为是的特征，并被视为量子理论的扩展。事实证明，在这些理论中，对两种类型的不确定性之间存在定量表达的连接：如果存在准备不确定性，则还存在测量不确定性，并且通过类似的不平等来描述它们。我们的结果表明，它们的对应关系不是量子理论的特定，而是更普遍的理论。
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and measurement uncertainty respectively, and research has unveiled that they are not independent from but related with each other in a quantitative way. This study aims to reveal whether similar relations to quantum ones hold also in generalized probabilistic theories (GPTs). In particular, a certain class of GPTs is considered which can be characterized by transitivity and self-duality and regarded as extensions of quantum theory. It is proved that there are close connections expressed quantitatively between two types of uncertainty on a pair observables also in those theories: if preparation uncertainty exists, then measurement uncertainty also exists, and they are described by similar inequalities. Our results manifest that their correspondences are not specific to quantum theory but more universal ones.
