Complete extension: the non-signaling analog of quantum purification

TL;DR

This paper introduces the complete extension postulate as a non-signaling analog to quantum purification, exploring its implications for general theories, including the impossibility of bit-commitment and properties of non-signaling behaviors.

Contribution

It proposes the complete extension postulate as a new foundational principle, extending quantum purification concepts to broader non-signaling theories and analyzing their consequences.

Findings

CEP implies the impossibility of bit-commitment

Non-signaling theories can satisfy CEP

Complete extensions may not always be pure

Abstract

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.