对称观测未必对应对称因果，不能随意缩小解释空间。
Symmetric observations without symmetric causal explanations
- 用三元二值概率分布验证对称性无法简化因果推断
- 即使放宽物理限制，对称性条件仍与观测相关性矛盾
- 适合研究因果推理与量子信息的学者参考
从观测相关性推断因果模型是科学中的关键挑战。为降低搜索可能因果解释的计算成本，需判断观测对称性是否反映底层机制的对称性。本文通过一个三元二值事件的概率分布实例证明：一般情况下，对称性无法用于缩小假设空间。该分布由三个独立的经典随机源实现。我们进一步证明，即使放弃经典物理假设，要求（i）各源产生相同物理系统，（ii）系统满足相对论因果性，（iii）相关性符合观测结果，这三个条件仍相互矛盾。
原文摘要 · Abstract (English)
Inferring causal models from observed correlations is a challenging task, crucial to many areas of science. In order to alleviate the computational effort when sifting through possible causal explanations for some given observations, it is important to know whether symmetries in the observations correspond to symmetries in the underlying realization so that one can quickly discard impossible explanations. Via an explicit example, we demonstrate that, in general, symmetries cannot be exploited to reduce the hypothesis space. We use a tripartite probability distribution over binary events that is realized by using three (different) independent sources of classical randomness. We prove that even removing the condition that the sources distribute systems described by classical physics, the requirements that (i) the sources distribute the same physical systems, (ii) these physical systems respect relativistic causality, and (iii) the correlations are the observed ones are incompatible.
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