发表机构
Università della Svizzera italiana; University of Vienna; Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences; Constructor University; University of Geneva; Mathematical Institute of the Serbian Academy of Sciences and Arts（瑞士意大利语大学; 维也纳大学; 奥地利科学院量子光学与量子信息研究所; 康斯特鲁克特大学; 日内瓦大学; 塞尔维亚科学与艺术学院数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对《选择公理与无信号原理》一文的评论，澄清了概率无信号策略的含义，指出选择公理构造的策略因不满足可测性要求而无法构成马尔可夫核。
AI 中文摘要
我们澄清了文献[Proc. R. Soc. A 481, 20240601]中概率无信号策略的含义。对于每个固定输入，运用选择公理构造的确定性策略确实可由输出上的狄拉克概率分布表示。当考虑从输入到输出的完整过程且输入自身按概率分布采样时，相关区别便会显现：此时输入与输出空间必须可测，条件输出分布对输入的依赖也需可测，等价于条件分布需构成马尔可夫核。选择公理构造的策略恰好不满足该可测性要求。
英文摘要
We clarify the meaning of a probabilistic no-signalling strategy in Ref [Proc. R. Soc. A 481, 20240601]. For every fixed input, the deterministic strategy constructed using the Axiom of Choice can indeed be represented by a Dirac probability distribution over the outputs. The relevant distinction arises when one considers the complete process from input to output, with the input itself sampled according to a probability distribution. In this case, the input and output spaces must be measurable and the dependence of the conditional output distribution on the input must also be measurable. Equivalently, the conditional distributions must form a Markov kernel. The Axiom-of-Choice strategy fails precisely this measurability requirement.
Comments2 pages; In press in Proc. R. Soc. A. Reply to arXiv:2604.20756
