Applicability of Renou et al.’s experimental falsification to all real-valued quantum theories

Determine whether the experimental falsification of real-number-based quantum theories claimed by Renou et al. (Nature 2021) via network Bell experiments applies to all real-valued formulations of quantum theory, rather than only to specific real-number frameworks.

Background

A 2021 result by Renou et al. claimed that any quantum theory formulated over real numbers can be experimentally falsified, using a network Bell experiment constructed to separate real and complex quantum predictions. This prompted the question of whether such a falsification genuinely rules out all conceivable real-valued reconstructions of quantum mechanics or only certain formulations.

The present paper argues that prior no-go results rely on an incomplete real formulation that adopts the standard real Kronecker product for composite systems, and proposes a Kähler-space-based real framework with a symplectic tensor product that is isomorphic to standard complex quantum mechanics. Against this backdrop, the authors explicitly note the open question of whether the earlier falsification extends to all real-valued theories.