Nonlocal quantum information transfer without superluminal signalling and communication

Abstract: It is a frequent assumption that - via superluminal information transfers - superluminal signals capable of enabling communication are necessarily exchanged in any quantum theory that posits hidden superluminal influences. However, does the presence of hidden superluminal influences automatically imply superluminal signalling and communication? The non-signalling theorem mediates the apparent conflict between quantum mechanics and the theory of special relativity. However, as a 'no-go' theorem there exist two opposing interpretations of the non-signalling constraint: foundational and operational. Concerning Bell's theorem, we argue that Bell employed both interpretations at different times. Bell finally pursued an explicitly operational position on non-signalling which is often associated with ontological quantum theory, e.g., de Broglie-Bohm theory. This position we refer to as "effective non-signalling". By contrast, associated with orthodox quantum mechanics is the foundational position referred to here as "axiomatic non-signalling". In search of a decisive communication-theoretic criterion for differentiating between "axiomatic" and "effective" non-signalling, we employ the operational framework offered by Shannon's mathematical theory of communication. We find that an effective non-signalling theorem represents two sub-theorems, which we call (1) non-transfer-control (NTC) theorem, and (2) non-signification-control (NSC) theorem. Employing NTC and NSC theorems, we report that effective, instead of axiomatic, non-signalling is entirely sufficient for prohibiting nonlocal communication. An effective non-signalling theorem allows for nonlocal quantum information transfer yet - at the same time - effectively denies superluminal signalling and communication.