Quantum from principles without assuming definite causal structure

There has been a body of works deriving the complex Hilbert space structure of quantum theory from axioms/principles/postulates to deepen our understanding about quantum theory and to reveal ways to go beyond it to resolve foundational issues. Recent progresses in incorporating indefinite causal structure into physical theories suggest that a more comprehensive understanding of both quantum theory and the theory beyond it accounts for indefinite causal structure. We formulate a framework of physical theories without assuming definite causal structure and identify postulates that single out the complex Hilbert space structure. More than one complex Hilbert space theory is compatible with the postulates, which leaves the room for the further search of the best among these theories.