用非投影可重复测量解释认知中的量子类现象
Quantum-like cognition and decision making in the light of quantum measurement theory
- 提出新型量子测量模型${\cal SR\bar{P}}$，适用于认知决策建模
- 发现状态更新非对易性是认知非经典性的关键机制
- 适合研究心理决策与量子类行为的学者参考
我们刻画了适用于认知（及决策）领域量子理论建模——量子类建模的量子测量类别。投影测量描述了量子物理基本可观测量的标准测量，但无法涵盖诸如问题顺序效应和回答可重复性等基本认知效应的组合。为此，我们提出使用一类特殊量子测量： { t sharp repeatable non-projective measurements}（${\cal SR\bar{P}}$），这类测量在量子物理中几乎未被使用，但在认知建模中具有重要意义。这表明物理与认知探索了量子测量理论的不同侧面。量子类建模并非简单借用量子形式体系。研究${\cal SR\bar{P}}$凸显了由测量反作用引发的状态更新映射之间的非对易性的重要作用。因此，量子物理中的‘非经典性’与认知领域的量子类建模，分别基于两种不同的非对易性：可观测量间的非对易性（ observable-noncommutativity）与仪器（状态更新映射）间的非对易性（ state update-noncommutativity）。我们推测，认知效应的量子类特征可能正是后者的体现，或两者兼有。
原文摘要 · Abstract (English)
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects, cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely {\it sharp repeatable non-projective measurements} - ${\cal SR\bar{P}}. $ This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modeling isn't automatic borrowing of the quantum formalism. Exploring the class ${\cal SR\bar{P}}$ highlights the role of {\it noncommutativity of the state update maps generated by measurement back action.} Thus, ``non-classicality'' in quantum physics as well as quantum-like modeling for cognition is based on two different types of noncommutativity, of operators (observables) and instruments (state update maps): {\it observable-noncommutativity} vs. {\it state update-noncommutativity}. We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.
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