论文标题
Wigner函数协方差与转换非上下文之间的关系
Relationship between covariance of Wigner functions and transformation noncontextuality
论文作者
论文摘要
我们研究了经常在量子理论的流行亚理论中研究的量子变换的两个属性之间的关系：理论的维格尔表示的协方差以及该理论的转化非文化本体论模型的存在。我们考虑由一组状态，测量和转换指定的量子理论的子理论，定义了指定一组单位的量子理论，这些量子理论是在子理论中的状态（和测量）之间映射的。我们表明，如果存在定义一组转换集的统一组的协变量的基理论的Wigner表示，则该子理论将接受转换非秘密本体论模型。我们提供了一些具体的论点来猜想，只要基本本体论模型是Wigner代表给出的，相反的语句也存在。此外，我们研究了协方差和转化非上下文性与该理论的准稳定性分布的存在，该理论代表转换为阳性保留图。我们得出结论，协方差意味着转变非上下文性，这意味着阳性保存。
We investigate the relationship between two properties of quantum transformations often studied in popular subtheories of quantum theory: covariance of the Wigner representation of the theory and the existence of a transformation noncontextual ontological model of the theory. We consider subtheories of quantum theory specified by a set of states, measurements and transformations, defined specifying a group of unitaries, that map between states (and measurements) within the subtheory. We show that if there exists a Wigner representation of the subtheory which is covariant under the group of unitaries defining the set of transformations then the subtheory admits of a transformation noncontextual ontological model. We provide some concrete arguments to conjecture that the converse statement also holds provided that the underlying ontological model is the one given by the Wigner representation. In addition, we investigate the relationships of covariance and transformation noncontextuality with the existence of a quasiprobability distribution for the theory that represents the transformations as positivity preserving maps. We conclude that covariance implies transformation noncontextuality, which implies positivity preservation.
