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Deriving quantum mechanics from information-theoretic postulates is a recentresearch direction taken, in part, with the view of finding a beyond-quantumtheory; once the postulates are clear, we can consider modifications to them. Akey postulate is the purification postulate, which we propose to replace by amore generally applicable postulate that we call the complete extensionpostulate (CEP), i.e., the existence of an extension of a physical system fromwhich one can generate any other extension. This new concept leads to aplethora of open questions and research directions in the study of generaltheories satisfying the CEP (which may include a theory that hyper-decoheres toquantum theory). For example, we show that the CEP implies the impossibility ofbit-commitment. This is exemplified by a case study of the theory ofnon-signalling behaviors which we show satisfies the CEP. We moreover show thatin certain cases the complete extension will not be pure, highlighting the keydivergence from the purification postulate.

Complete extension: the non-signaling analog of quantum purification