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