Ozawa Masanao, Khrennikov Andrei
Graduate School of Informatics, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan.
College of Engineering, Chubu University, 1200 Matsumoto-cho, Kasugai 487-8501, Japan.
Entropy (Basel). 2019 Dec 26;22(1):37. doi: 10.3390/e22010037.
Recently, quantum formalism started to be actively used outside of quantum physics: in psychology, decision-making, economics, finances, and social science. Human psychological behavior is characterized by a few basic effects; one of them is the question order effect (QOE). This effect was successfully modeled (Busemeyer-Wang) by representing questions and by Hermitian observables and mental-state transformations (back action of answering) by orthogonal projectors. However, then it was demonstrated that such representation cannot be combined with another psychological effect, known as the response replicability effect (RRE). Later, this no-go result was generalized to representation of questions and state transformations by quantum instruments of the atomic type. In light of these results, the possibility of using quantum formalism in psychology was questioned. In this paper, we show that, nevertheless, the combination of the QOE and RRE can be modeled within quantum formalism, in the framework of theory of non-atomic quantum instruments.
最近，量子形式主义开始在量子物理学之外被积极应用：在心理学、决策、经济学、金融和社会科学领域。人类的心理行为具有一些基本效应；其中之一是问题顺序效应（QOE）。通过用厄米算符表示问题以及用正交投影算符表示心理状态变换（回答的反向作用），这种效应被成功建模（布瑟迈尔 - 王模型）。然而，随后证明这种表示不能与另一种心理效应，即反应可重复性效应（RRE）相结合。后来，这个不可行结果被推广到由原子型量子仪器表示问题和状态变换的情况。鉴于这些结果，在心理学中使用量子形式主义的可能性受到质疑。在本文中，我们表明，尽管如此，在非原子量子仪器理论的框架内，QOE和RRE的组合可以在量子形式主义中建模。
