标题： 算术序列作为量子态 显示英文标题

标题： Arithmetic sequences as quantum states

摘要： 我们考虑算术序列，这里定义为正整数的有序列表。 任何这样的序列都可以映射到一个量子态，从而通过冯·诺依曼熵量化其“意外性”。 我们识别出在所有二分划分中最大化纠缠熵的典型序列，并推导出一个关于序列长度的解析近似值。 这种受量子启发的方法为分析算术序列中的随机性提供了新的视角。 显示英文摘要

摘要： We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical sequences that maximize entanglement entropy across all bipartitions and derive an analytical approximation as a function of the sequence length. This quantum-inspired approach offers a novel perspective for analyzing randomness in arithmetic sequences.