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极简决策动力学与上下文概率：量子拔河模型

文章背景与核心概要

本文探讨了人类和智能体在决策过程中表现出的“上下文依赖性”（Context-dependence），并评估了这种特性是否可以用单一、受限的内部状态来表示，而无需引入复杂的非侵入式经典概率模型。作者提出了量子拔河模型（Quantum Tug-of-War, QTOW）的类量子扩展，采用三能级量子态（qutrit）状态空间，展示了广义决策仪器、保范反馈以及探针操作如何违反非上下文性边界（如KCBS型不等式）。

研究并非断言量子理论直接源于决策机制，而是揭示了自然与人工智能中一个根本性的架构权衡：上下文信息既可以通过共享内部状态的变换以内在方式携带，也可以外化到补充的状态和内存资源中。这一发现为理解认知架构中的状态表示与内存资源分配提供了新的视角。

最小决策动力学与上下文概率：量子拔河模型 (Minimal Decision Dynamics and Contextual Probability: A Quantum Tug-of-War Model)

摘要 (Summary)

本文研究了上下文相关的决策制定，并评估了是否可以使用单一、受限的内部状态（而非复杂的非侵入式经典概率模型）来表示这种决策。通过在三能级量子态（qutrit）状态空间中引入拔河（Tug-of-War, QTOW）决策模型的类量子扩展，作者展示了广义决策仪器、保范反馈和探针操作如何违反非上下文性边界（例如 KCBS 型不等式）。

该研究并非认为量子理论独特地源于决策制定，而是强调了自然和人工智能中一个基本的架构权衡：上下文信息可以通过共享内部状态的变换以内在方式携带，或者外化为补充的状态和内存资源。

This paper investigates context-dependent decision-making and evaluates whether it can be represented using a single, constrained internal state rather than requiring complex non-invasive classical probability models. Introducing a quantum-like extension of the Tug-of-War (QTOW) decision-making model using a qutrit state space, the author demonstrates how generalized decision instruments, norm-preserving feedback, and probe operations violate non-contextuality bounds (such as KCBS-type inequalities).

Rather than arguing that quantum theory is uniquely derived from decision-making, the study highlights a fundamental architectural trade-off in natural and artificial intelligence: contextual information can either be carried intrinsically via transformations of a shared internal state or externalized into supplementary state and memory resources.

文档元数据 (Document Metadata)

字段 (Field) 详情 (Details)
arXiv ID arXiv:2601.10034 [quant-ph]
标题 (Title) Minimal Decision Dynamics and Contextual Probability: A Quantum Tug-of-War Model
作者 (Author) Song-Ju Kim
主要学科 (Primary Subject) 量子物理 (quant-ph)
交叉学科 (Cross-Subjects) 人工智能 (cs.AI)、神经元与认知 (q-bio.NC)
时间线 (Timeline) 2026年1月15日提交；2026年8月25日最后修订 (v3)
DOI 10.48550/arXiv.2601.10034
Field Details
arXiv ID arXiv:2601.10034 [quant-ph]
Title Minimal Decision Dynamics and Contextual Probability: A Quantum Tug-of-War Model
Author Song-Ju Kim
Primary Subject Quantum Physics (quant-ph)
Cross-Subjects Artificial Intelligence (cs.AI), Neurons and Cognition (q-bio.NC)
Timeline Submitted on 15 Jan 2026; Last revised 25 Aug 2026 (v3)
DOI 10.48550/arXiv.2601.10034

摘要 (Abstract)

决策制定通常表现出上下文依赖性，这很难在单个非侵入式经典概率模型中得到满足。本文开发了拔河（Tug-of-War, QTOW）决策模型的类量子扩展，探讨何时可以用单一受限的内部状态来表示这种上下文依赖性。

QTOW 结构使用了一个三能级量子态、一个会干扰状态的广义决策仪器、受决策和奖励条件制约的保范反馈，以及在单个状态空间内的可选探测操作。该三能级表示允许 KCBS 类型的探针族和违反非上下文性边界的状态，这提供了一个凭证，证明指定的操作系统无法嵌入到单一的非上下文经典概率空间中。

该主张并非认为量子理论独一无二地源于决策制定。经典重建可以通过引入明确的上下文标签、存储的历史记录或扩大的状态描述来保持描述的充分性；或者，通过限制允许的探针集来避免非上下文性凭证。相反，量子概率为这里考虑的上下文操作系列提供了一个紧凑的单状态实现。

从自然和人工智能的角度来看，该结果确定了一个架构级别的表征权衡：上下文信息可以由共享内部状态的变换以内在方式携带，或者外化到额外的状态和内存资源中。

Decision making often exhibits context dependence that is difficult to accommodate within a single non-invasive classical probability model. This paper develops a quantum-like extension of the Tug-of-War (QTOW) decision-making model to ask when such context dependence can be represented by a single constrained internal state.

The QTOW construction uses a qutrit state, a state-disturbing generalized decision instrument, decision- and reward-conditioned norm-preserving feedback, and optional probing operations within one state space. The qutrit representation admits KCBS-type probe families and states that violate a non-contextuality bound, providing a witness that the specified operation family cannot be embedded in a single non-contextual classical probability space.

The claim is not that quantum theory is uniquely derived from decision making. Classical reconstructions can retain descriptive adequacy by introducing explicit context labels, stored history, or enlarged state descriptions; alternatively, the non-contextuality witness can be avoided by restricting the admissible probe set. Quantum probability instead supplies a compact single-state realization of the contextual operation family considered here.

From the perspective of natural and artificial intelligence, the result identifies an architecture-level representational trade-off: contextual information may be carried intrinsically by transformations of a shared internal state or externalized into additional state and memory resources.

核心亮点与修订 (v3) (Key Highlights & Revisions (v3))

  • QTOW 学习动力学 (QTOW Learning Dynamics)： 使用广义决策仪器以及受决策和奖励条件制约的反馈进行公式化。
  • 上下文分析 (Contextuality Analysis)： 阐明了 KCBS 型边界的存在，证明了其无法嵌入经典概率空间。
  • AI 与认知影响 (AI & Cognitive Implications)： 在状态表示与内存资源分配方面，建立了量子力学与认知架构（自然与人工智能）之间的桥梁。
  • QTOW Learning Dynamics: Formulated using a generalized decision instrument alongside decision- and reward-conditioned feedback.
  • Contextuality Analysis: Clarified the presence of KCBS-type bounds proving non-embeddability into classical probability spaces.
  • AI & Cognitive Implications: Bridge established between quantum mechanics and cognitive architectures (natural and artificial intelligence) regarding state representation versus memory resource allocation.

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