[论文解读] Embedding cyclic information-theoretic structures in acyclic spacetimes: no-go results for indefinite causality

V. Vilasini, Renato Renner|arXiv (Cornell University)|Mar 21, 2022

Quantum Mechanics and Applications被引用 13

一句话总结

本文通过证明在无环时空中无法一致地嵌入非局域系统时，解决了量子过程中不定因果顺序（ICO）与确定性时空因果性之间的表观悖论。利用将信息理论因果性与相对论因果性相联系的图论框架，作者证明了不可行定理：ICO 实现需要时空非局域化，并且在细致分析下可获得明确的、无环的因果解释，从而完全调和了 ICO 实验与相对论之间的矛盾。

ABSTRACT

The notions of causality adopted within the quantum information and spacetime physics communities are distinct. Although both notions play a role in physical experiments, their general interplay is little understood in theory. We develop a theoretical framework that connects the two causality notions, while also clearly distinguishing them. The framework describes a composition of quantum operations through feedback loops, and the embedding of the resulting, possibly cyclic information-theoretic structure in an acyclic spacetime structure. Relativistic causality (which forbids superluminal communication) follows as a graph-theoretic compatibility condition between the two structures. Formulating indefinite causal order (ICO) processes in our framework, we shed light on the links between indefinite and cyclic causality, and on questions regarding their physicality. In particular, there are several experiments that claim to implement ICO processes in Minkowski spacetime, presenting an apparent paradox: how can an indefinite information-theoretic causal structure be consistent with a definite spacetime causal structure? We address this through no-go theorems, showing that as a consequence of relativistic causality, (a) realisations of ICO processes necessarily involve the non-localisation of systems in spacetime and (b) will nevertheless admit an explanation in terms of a definite and acyclic causal order process, at a fine-grained level. This fully resolves the apparent paradox and bears implications for the physical interpretation of ICO experiments, and is achieved by introducing the concept of fine-graining that allows causal structures to be analysed at different levels of detail. Our work also sheds light on the limits of quantum information processing in spacetime and on the operational meaning of indefinite causality, within and beyond the context of a fixed spacetime.

研究动机与目标

• 澄清信息理论因果性（例如，不定因果顺序）与相对论因果性（无超光速信号）之间的相互作用。
• 解决实验中声称在具有确定因果结构的闵可夫斯基时空中实现不定因果顺序的表观矛盾。
• 建立一个统一框架，通过图论相容性条件区分并连接两种因果性概念。
• 研究在固定时空中背景（特别是闵可夫斯基时空）中实现不定因果顺序过程的物理可行性。

提出的方法

• 形式化具有反馈回路的量子过程组合，以模拟循环的信息理论结构。
• 引入图论框架，将信息理论因果结构和时空因果结构均表示为有向图。
• 将相对论因果性定义为两种图之间的相容性条件，禁止超光速信号。
• 将该框架应用于分析不定因果顺序（ICO）过程及其在无环时空中嵌入的问题。
• 引入“精细划分”概念，以不同细节层次分析因果结构，揭示其底层的无环顺序。
• 利用该框架推导出关于 ICO 过程在确定性时空中物理一致性的不可行定理。

实验结果

研究问题

• RQ1 在不违反相对论因果性的情况下，不定因果顺序过程能否在无环时空中一致地实现？
• RQ2 在量子过程中，信息理论因果性与相对论因果性之间存在何种操作关系？
• RQ3 如何调和声称在闵可夫斯基时空中实现 ICO 的实验与时空的确定性因果结构之间的矛盾？
• RQ4 在无环时空中嵌入循环信息理论结构时会产生何种物理约束？
• RQ5 通过细致的因果分析，表观的不定因果性悖论在确定性时空中能在多大程度上被解决？

主要发现

• 根据相对论因果性要求，不定因果顺序（ICO）过程若无时空非局域化的量子系统，则无法在无环时空中一致实现。
• 尽管在粗粒度层次上表现出不定因果顺序，但所有 ICO 过程在精细粒度分析下均可获得明确的、无环的因果顺序解释。
• 该框架表明，相对论因果性在信息理论因果结构与时空因果结构之间施加了图论相容性条件。
• 不可行定理表明，任何在闵可夫斯基时空中实现 ICO 过程的情形，都必须涉及在时空中非局域化的系统。
• 精细划分概念使得因果结构可在多个层次上被分析，揭示出不定因果性是粗粒度层次上的涌现特征。
• 该框架确认了 ICO 实验的物理解释与相对论一致，通过结构分解解决了表观悖论。