量子非定域性在经典模拟中需付出额外信息代价。
Contextuality as an External Bookkeeping Cost under Fixed Shared-State Semantics
- 用辅助标签记录上下文依赖，量化经典模拟所需额外信息量。
- 证明任何线性判别式都能给出外部记账成本的下界。
- 揭示量子特性背后不可简化的信息开销，适合理论物理与量子信息研究者。
上下文性是量子与经典概率理论的核心区别，但其操作意义常仅以定性描述。本文研究一个简单信息论问题：当经典模拟试图在不同上下文中保持内部描述一致时，需引入多少额外的上下文信息？为此，我们分析一种最小外部标签模拟模型，其中剩余上下文依赖仅由辅助标签承载。定义阻碍成本为上下文与辅助标签间的最小互信息，以重现观测统计。我们证明：任何能将观测统计与零阻碍集分离的线性见证，均给出该成本的保守定量下界。该下界未必紧致，模型也未涵盖所有经典架构。其作用更局限而明确：在固定共享态语义下，上下文性可被解读为简单且明确模拟模型中不可减少的外部记账成本的证言。
原文摘要 · Abstract (English)
Contextuality is a central feature distinguishing quantum from classical probability theories, but its operational meaning is often stated only qualitatively. In this Letter, we study a simple information-theoretic question: how much additional contextual information must a classical simulation introduce when it tries to keep a shared internal description fixed across contexts? To make this question precise, we analyze a minimal external-label simulation model in which the remaining context dependence is carried only by an auxiliary label. For this model, we define an obstruction cost as the minimum mutual information between the context and the auxiliary label required to reproduce the observed statistics. We then prove a conservative quantitative lower bound: any linear witness that separates the observed statistics from the zero-obstruction set yields a positive lower bound on this cost. We do not claim that this bound is tight, and we do not claim that the simulation model covers every possible classical architecture. Its role is narrower and more explicit: under fixed shared-state semantics, contextuality can be read as a certificate of irreducible external bookkeeping cost in a simple and well-defined simulation model.
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