不确定条件下的非决定性量子测量和决策
Inconclusive quantum measurements and decisions under uncertainty
摘要：
我们给出了非决定性量子测量概念的数学定义。在物理学中，这种测量发生在复杂测量过程的中间阶段，最终的测量结果是可操作测试的。由于量子决策理论的数学结构是以类似于量子测量理论的方式发展起来的，因此在量子决策理论中，不确定的量子测量对应于在不确定性下做出决策的过程中的决策制定的中间阶段。复合事件的量子概率的一般形式是效用因子和吸引因子的总和，效用因子描述了对所考虑的前景的理性评估，吸引因子表征了决策者的非理性、潜意识态度。尽管存在不合理性，但前景的可能性是可以评估的。这相当于在不指定隐变量的情况下计算量子概率的可能性。我们制定了一个一般的评价方式，基于使用非信息先验。作为一个例子，我们建议解释诱饵效应。我们的定量预测与实验数据非常吻合。
英文摘要：
We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in Quantum Decision Theory, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.
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