Quantum Probability from Decision Theory?
J. Finkelstein
Deutsch最近（在quant-ph/9906015中）仅根据量子理论和经典决策理论的非概率公理，为使用标准量子概率规则提供了一个理由。本说明将审查这一理由。
Deutsch has recently (in quant-ph/9906015) offered a justification, based only on the non-probabilistic axioms of quantum theory and of classical decision theory, for the use of the standard quantum probability rules. In this note, this justification is examined.
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Quantum Probability and Decision Theory, Revisited
扩展分析的程序，最初建议的Deutsch，解决概率问题的埃弗雷特解释的决策理论的手段。Deutsch自己的证明进行了讨论，并提出了替代品是基于不同的决策理论和格里森定理。有人认为，决策理论给埃弗雷特人的大部分或全部，他们需要从'概率'。一些后果（埃弗雷特）量子力学的决策理论本身进行了讨论。
Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?
批评者反对说，埃弗雷特的观点不能理解量子概率，在两个方面中的一个或两个方面：要么它根本不能理解概率，要么它不能解释为什么概率应该由玻恩规则支配。大卫·多伊奇（David Deutsch）试图通过诉诸萨维奇理性决策理论的埃弗雷特版本来回应这些反对意见。多伊奇不仅认为，在埃弗雷特世界中，不确定性下的经典决策的类似物是有意义的;而且在合理的假设下，理性埃弗雷特代理人的下注几率应该受到波恩规则的约束。多伊奇的提议得到了大卫·华莱士的辩护和发展，并以不同的形式得到了希拉里·格里夫斯的辩护和发展。在本文中，我提供了一些反对德意志-华莱士-格里夫斯的论点，特别是集中在假设的类比与经典的决定下的不确定性。
Quantum Theory of Probability and Decisions
量子理论的概率预言通常是从一个特殊的概率公理中得到的。但这是不必要的，因为这些预测的所有实际结果都来自量子理论剩余的非概率公理，以及经典决策理论的非概率部分。
Quantum Probability from Decision Theory?
在最近的一篇论文（quant-ph/9906015）中，多伊奇声称从“量子理论的非概率公理“和“经典决策理论的非概率部分”推导出“量子理论的概率预测“。“我们证明他的推导失败了，因为它包含了隐藏的概率假设。
Minimum Decision Cost for Operators
以最小化错误概率为目标的状态判别是一个很好的研究问题。相反，这里的二元决策问题的运营商与一个给定的先验研究。用选定的波函数探测包含未知算子的黑盒。输出分析与传统的方法开发的状态歧视。所有的二元算子的选择提供了一个错误的概率界，它是如何探测纠缠增强的结果。
Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule
我提出了一个证明的量子概率规则从决策理论的假设，在埃弗雷特解释的上下文中。这个证明背后的基本思想是Deutsch最近对概率规则的证明中提出的，但是这个证明更简单，并且从较弱的决策理论假设出发。这使得讨论证明中涉及的概念思想更容易，并表明它们是可辩护的。
Another look at the optimal Bayes cost in the binary decision problem
考虑了方势阱中粒子的两个波函数之间的量子态判别问题。已知状态判别的最优最小误差概率由Helstrom界给出。一个新的策略是在这里引入的方井被压缩等能，修改波函数。然后用传统的最优策略对新的收缩腔进行探测，并计算了误差概率。结果表明，在某些情况下，可以违反Helstrom界，即状态判别可以实现较小的错误概率。
Quantum theory of measurements as quantum decision theory
量子测量理论通常被归类为决策理论。决策理论中的事件对应于可观测的度量。这种类比对于可操作测试的简单事件看起来很清楚。然而，在复合事件的情况下，情况基本上更为复杂。最困难的一点是不确定性下的决策和不确定性下的测量之间的关系。我们建议一个统一的语言来描述量子决策和量子测量的过程。介绍了不确定度下的量子测量概念。我们表明，正确的数学基础下的测量理论的不确定性，以及量子决策理论处理不确定事件，需要使用积极的算子值的措施，这是一个推广的投影值措施。后者适用于作战上可检验的事件，而前者是表征作战上不确定事件所必需的。在决策和量子测量中，必须区分复合非纠缠事件和复合纠缠事件。只有对于纠缠事件，量子概率才与经典概率有本质上的不同。在量子概率中出现干涉项的必要条件是纠缠前景的出现以及决策者的纠缠策略态或测量设备的纠缠统计态的存在。
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting observables in addition to commutative observables. Our proposed definition of quantum probability makes it possible to describe quantum measurements and quantum decision making on the same common mathematical footing. Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of qu…
Understanding Deutsch's probability in a deterministic multiverse
概率的困难常常被认为是对量子力学的埃弗雷特解释的致命打击。在这里，我认为，埃弗雷特人可以从“概率”中获得她所需要的一切，而不必求助于非决定论、无知、随着时间的推移的原始同一性或主观的不确定性：她所需要的只是一个特定的合理性原则。Deutsch和Wallace最近发展的决策理论方法声称提供了这样一个原则。但是，根据华莱士的观点，只有当对未来埃弗雷特测量结果的正确态度是主观的不确定性时，决策理论本身才适用。我认为，主观的不确定性是没有的，但我提供了另一种解释，使埃弗雷特生活没有不确定性：我们可以证明埃弗雷特决策理论的基础上，埃弗雷特应该 * 关心 * 她的所有未来分支。出现在决策论表示定理中的概率可以解释为理性主体关心每个未来分支的程度。然而，这种重新解释降低了Deutsch-Wallace公理之一（测量中性）的直观可解释性。
Contextual Probability and Operational Minimality in Tug-of-War Decision Making
研究决策中上下文依赖挑战经典概率论的问题，通过开发QTOW决策模型扩展，用特定量子构建在相干空间建模相关操作，表明上下文概率是最小决策动力学资源特征，量子概率提供紧凑实现。
Quantum Computation Based Probability Density Function Estimation
在不久的将来，信号处理技术将依赖于盲方法，其中不会通过信道传输冗余的资源分配信息。然而，为了实现正确的决策，必须至少知道概率密度函数（pdf），估计该概率密度函数通常是耗时的和/或不太准确的硬任务，其可能使决策失败。本文还通过一个例子描述了一种量子辅助概率密度函数估计方法的设计，该方法通过适当地设置参数可以非常快速地获得精确的概率密度函数。
The problem of quantum state discrimination between two wave functions on a ring is considered. The optimal minimum-error probability is known to be given by the Helstrom bound. A new strategy is introduced by inserting either adiabatically or instantaneously an impenetrable barrier. The insertion point, independent of the shape of the initial wave function, becomes a node. The resulting modified wave functions can be, if the initial functions are judiciously chosen, distinguished with a smaller error probability, and as a consequence the Helstrom bound can be violated under idealised conditio…
Unitary quantum theory, having no Born Rule, is non-probabilistic. Hence the notorious problem of reconciling it with the unpredictability and appearance of stochasticity in quantum measurements. Generalising and improving upon the so-called 'decision-theoretic approach' (Deutsch, 1999; Wallace, 2003, 2007, 2012), I shall recast that problem in the recently proposed constructor theory of information - where quantum theory is represented as one of a class of superinformation theories, which are local, non-probabilistic theories conforming to certain constructor-theoretic conditions. I prove tha…
We present an experimental illustration on the quantum sensitivity of decision making machinery. In the decision making process, we consider the role of available information, say hint, whether it influences the optimal choices. To the end, we consider a machinery method of decision making in a probabilistic way. Our main result shows that in decision making process our quantum machine is more highly sensitive than its classical counterpart to the hints we categorize into "good" and "poor." This quantum feature originates from the quantum superposition involved in the decision making process. …
Quantum Ordered Binary Decision Diagrams with Repeated Tests
量子分支程序（量子二元决策图）是一个方便的工具，用于检查量子计算只使用对数数量的空间。最近几种类型的限制量子分支程序已被考虑，例如。G.只读一次量子分支程序。本文考虑量子有序二元决策图（QOBDDs），并回答了这样一个问题：如果我们允许重复测试，QOBDDs的计算能力如何增加。此外，它描述了如何合成QOBDD根据布尔运算。
Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation
一个分析是由德意志最近声称已得出波恩规则的决策理论的假设。有人认为，德意志的证明必须理解的明确背景下的埃弗雷特解释，并在这种情况下，它基本上成功。一些评论是关于批评德意志的证明巴纳姆，洞穴，芬克尔斯坦，富克斯，和沙克;有人认为，缺陷，他们指出的证据不适用，如果埃弗雷特解释是假设。这篇论文的一个更长的版本，题为“量子概率和决策理论，修订”，也可以在网上找到。
In this paper it is proposed the dynamical quantum Zeno Effect in quantum decision theory. The measurement postulate is not an essential ingredient for the explanation of the quantum Zeno effect, a dynamical account is given in quantum physics. In this account, the entanglement between the system of interest and the apparatus inhibit the quantum transition. The collapse postulate is not considered. It is show in this paper that the belief-action entanglement model provides a mathematical framework for the dynamical quantum Zeno effect in quantum decision theory. It is also shown that, in this …
On the solution of trivalent decision problems by quantum state identification
三价体的三价功能可以分为三个元素的均分。我们讨论了用量子态标识分离相应的泛函类。
Quantum random number generator based on the photon number decision of weak laser pulses
提出了一种基于弱激光脉冲光子数决定的量子随机数发生器的实现方法。这种量子随机数发生器具有产生真随机数的速度快、零偏调节方便等优点，适合于量子密码学中的应用。
Quantum probability measures and tomographic probability densities
最近提出的基于量子态层析概率分布的方法与量子信息理论中讨论的量子概率测度和正算子值测度方法密切相关。证明了与零差求积（辛量子测度）相关联的量子概率测度的分布函数的偏导数等于量子态的层析图。得到了自旋断层像与自旋态量子概率测度的类似关系。研究了辛量子测度的星积。导出了辛量子测度的演化方程。
Reexamination of the optimal Bayes cost in the binary decision problem
考虑了方势阱中粒子的两个波函数之间的量子态判别问题。已知最优最小误差概率由Helstrom界给出。通过在方阱中间插入一个不可穿透的屏障，引入了一种新的策略，该屏障可以是波函数的节点或非节点。插入势垒所需的能量取决于初始状态。这使得实验者能够获得超出Helstrom所设想的状态的标准探测的额外信息，并提高状态的可解释性。结果表明，在一定条件下，可以违反Helstrom界，即状态判别可以实现较小的错误概率。
Almost all decision trees do not allow significant quantum speed-up
我们表明，对于任何d，除了一个双指数小部分的决策树的深度最多d需要Ω（d）量子查询计算有界误差。换句话说，在查询复杂度模型中，大多数有效的经典算法不允许显著的量子加速。证明是基于显示，具有高概率，随机决策树的平均灵敏度高。
The sure thing principle and the law of total probability are basic laws in classic probability theory. A disjunction fallacy leads to the violation of these two classical probability laws. In this paper, a new quantum dynamic belief decision making model based on quantum dynamic modelling and Dempster-Shafer (D-S) evidence theory is proposed to address this issue and model the real human decision-making process. Some mathematical techniques are borrowed from quantum mathematics. Generally, belief and action are two parts in a decision making process. The uncertainty in belief part is represen…
Modeling the Disjunction Effect within Classical Probability: A New Decision Process Model and Comparison with Quantum-like Models
本文提出一种新的经典决策模型，通过连续期望参数和分层期望池来处理不确定性，证明其能实现任意观察到的背叛率三元组，同时严格遵守经典概率定律，与量子类模型在可观察率表达上具有相同能力。
Quantum decision theory as quantum theory of measurement
我们提出了量子信息处理设备的一般理论，可以应用于人类决策者，原子多模寄存器，或分子高自旋寄存器。我们的量子决策理论是测量的量子理论的推广，赋予了一个作用环，一个前景格和一个概率算子测度。概率算子的代数起着局部可观量的代数的作用。由于前景的复合性质和概率算符的纠缠性质，量子干涉项出现了，这使得作用是非对易的，前景概率是非加性的。该理论为解释经典效用理论在实际人类决策中的典型应用中的各种悖论提供了基础。我们的方法的主要优点是，它被制定为一个自洽的数学理论，这使我们能够解释不只是一个效果，但实际上所有已知的悖论在人类决策。该方法具有通用性，可作为表征原子、分子和凝聚态系统量子信息处理的工具。
Categorization is necessary for many decision making tasks. However, the categorization process may interfere the decision making result and the law of total probability can be violated in some situations. To predict the interference effect of categorization, some model based on quantum probability has been proposed. In this paper, a new quantum dynamic belief (QDB) model is proposed. Considering the precise decision may not be made during the process, the concept of uncertainty is introduced in our model to simulate real human thinking process. Then the interference effect categorization can …
We propose a quantum expected value theory for decision-making under uncertainty. Quantum density operator as value operator is proposed to simulate people's subjective beliefs. Value operator guides people to choose corresponding actions based on their subjective beliefs through objective world. The value operator can be constructed from quantum gates and logic operations as a quantum decision tree. The genetic programming is used to optimize and auto-generate quantum decision trees.
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…
Interference and inequality in quantum decision theory
量子决策理论是在其最简单的形式两个条件两个选择设置检查。一组不等式所满足的任何量子条件概率描述的决策过程的推导。实验数据表明，经典的解释的故障严格审查与量子理论使用全套的量子相位。
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between separate alternatives, sequential alternatives characterizing conditional quantum probabilities, and behavioral quantum probabilities taking into account rational-irrational duality of decision making. The comparison between quantum and classical probabilities is explained. The analysis demonstrates that quantum probabilities serve as an essentially more powerful …
This work is related to the implementation of a decision tree construction algorithm on a quantum simulator. Here we consider an algorithm based on a binary criterion. Also, we study the improvement capability with quantum heuristic QAOA. We implemented the classical and the quantum version of this algorithm to compare built trees.
This study utilises an experiment famous in quantum physics, the Stern-Gerlach experiment, to inform the structure of an experimental protocol from which a quantum cognitive decision model can be developed. The 'quantumness' of this model is tested by computing a discrete quasi-probabilistic Wigner function. Based on theory from quantum physics, our hypothesis is that the Stern-Gerlach protocol will admit negative values in the Wigner function, thus signalling that the cognitive decision model is quantum. A crowdsourced experiment of two images was used to collect decisions around three questi…
Open systems, quantum probability and logic for quantum-like modeling in biology, cognition, and decision making
本综述探讨了应用量子理论的数学形式体系对宏观复杂生物系统进行类量子建模的可能性，强调基于开放量子系统理论（如量子仪器和量子主方程）来处理生物与心理过程的信息，并指出QBism可能是最有用的解释。
Due to the rapid development of quantum computing, the compact representation of quantum operations based on decision diagrams has been received more and more attraction. Since variable orders have a significant impact on the size of the decision diagram, identifying a good variable order is of paramount importance. In this paper, we integrate linear transformations into an efficient and canonical form of quantum computing: Quantum Multiple-Valued Decision Diagrams (QMDDs) and develop a novel canonical representation, namely linearly transformed QMDDs (LTQMDDs). We design a linear sifting algo…
Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides …
The review presents the basics of quantum decision theory, with the emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. The difference of an operationally testable rational choice between alternatives from a choice decorated by irrational feelings is elucidated. Quantum-classical correspondence is emphasized. A model of quantum intelligence network is described. Dynamic inconsistencies are shown to be resolved in the frame of the quantum decision theory.
Processing Information in Quantum Decision Theory
综述了量子决策理论中描述信息处理的最新进展，量子决策理论是基于可分希尔伯特空间的数学理论提出的一种新的决策方法。这种数学结构捕捉复合前景叠加的效果，包括许多合并的预期行动。该理论的特点纠缠决策，非交换性的后续决策，意图干扰。量子决策理论框架下的自洽决策过程既考虑了客观信息，也考虑了主观的情境效应。这种量子方法避免了经典决策理论中的任何典型悖论。条件最大化的熵，相当于最小化的信息功能，使人们有可能连接量子和经典的决策理论，表明后者是前消失的干扰项下的限制。
Despite the impressive success of quantum structures to model long-standing human judgement and decision puzzles, the {\it quantum cognition research programme} still faces challenges about its explanatory power. Indeed, quantum models introduce new parameters, which may fit empirical data without necessarily explaining them. Also, one wonders whether more general non-classical structures are better equipped to model cognitive phenomena. In this paper, we provide a {\it realistic-operational foundation of decision processes} using a known decision-making puzzle, the {\it Ellsberg paradox}, as …
{\it Ellsberg thought experiments} and empirical confirmation of Ellsberg preferences pose serious challenges to {\it subjective expected utility theory} (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions under uncertainty which satisfactorily copes with the Ellsberg paradox and other puzzles of SEUT. We apply here the quantum-theoretic framework to the {\it Ellsberg two-urn example}, showing that the paradox can be explained by assuming a state change of the conceptual entity that is the object of the decision ({\it decision-making}, or {\it DM}, {\it entity…
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