Locality Implies Complex Numbers in Quantum Mechanics

Abstract

We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number quantum theory is equivalent to a real-number quantum theory with hidden nonlocal degrees of freedom. Our results suggest that complex numbers may be indispensable for describing the process involving entanglement between two independent systems.

arXiv comment7 pages