广义概率论中反射超平面上的共存性
Coexistence on Reflecting Hyperplane in Generalized Probability Theories
摘要：
研究了一类广义概率论中效应的共存性。对应于偶数边正多边形状态空间的效应空间具有包含所有非平凡极值效应的中心超平面。这样一个超平面的存在，称为反射超平面，与相应状态空间的点对称性密切相关。在这样一个超平面上的效应可以被认为是（广义）无偏效应。给出了偶数边正多边形理论中存在一对无偏效应的充分必要条件。这一结果在一定限度内再现了量子比特效应已知结果的低维模拟。
英文摘要：
The coexistence of effects in a certain class of generalized probability theories is investigated. The effect space corresponding to an even-sided regular polygon state space has a central hyperplane that contains all the nontrivial extremal effects. The existence of such a hyperplane, called a reflecting hyperplane, is tightly related to the point symmetry of the corresponding state space. The effects on such a hyperplane can be regarded as the (generalized) unbiased effects. A necessary and sufficient condition for a pair of unbiased effects in the even-sided regular polygon theories is presented. This result reproduces a low-dimensional analogue of known results of qubit effects in a certain limit.
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