标题： 局部性蕴含量子力学中的复数 显示英文标题

标题： Locality Implies Complex Numbers in Quantum Mechanics

摘要： 我们证明了与独立源假设相容的实数量子理论需要包含一个非局部映射。 这意味着，如果独立源假设成立，则复数量子理论等价于具有隐藏非局部自由度的实数量子理论。 这一结果表明，描述涉及两个独立系统纠缠的过程时，复数是不可或缺的。 也就是说，量子理论从根本上需要复数；否则，人们可能不得不接受非局部的实数量子理论。 显示英文摘要

摘要： We show that a real-number quantum theory, compatible with the independent source assumption, requires the inclusion of a nonlocal map. This means that if the independent source assumption holds, complex-number quantum theory is equivalent to a real-number quantum theory with hidden nonlocal degrees of freedom. This result suggests that complex numbers are indispensable for describing the process involving entanglement between two independent systems. That is, quantum theory fundamentally requires complex numbers; otherwise, one may have to accept a nonlocal real-number quantum theory.