A local real-valued formulation of quantum mechanics

A fundamental question of necessity of use of complex numbers in quantum mechanics has a long history. Recently it was claimed that any formulation of quantum mechanics based on real numbers either is unable to reproduce certain multipartite Bell-type experiments or violates certain postulates. We show that a physically motivated postulate about composite quantum systems that respect locality allows to construct quantum mechanics based on real numbers that reproduces predictions for all multipartite quantum experiments. Thus, formally, we can say that the use complex numbers is a matter of convenience. From the other side, the proposed real-valued construction still emulates the complex structure and in this sense it is fundamental.