Nonlocal Quantum Information Transfer Without Superluminal Signalling and Communication

Jan Walleczek,Gerhard Grössing

doi:10.1007/s10701-016-9987-9

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.

Highlights

Bell’s theorem proved that no quantum theory based on the joint assumptions of “causality and locality” can successfully reproduce the predictions that are yielded by orthodox quantum mechanics [1]
The impossibility to signal by way of superluminal influences Bell took to be the central issue for any explanatory, causal approaches to quantum mechanics [7]: “For me this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity.”
Having in hand a single criterion for the consistent differentiation between axiomatic non-signalling and effective non-signalling, questions to be explored in future work include the following: Does the proposition of nonlocal information transfer automatically entail a space-time structure that ceases to be Lorentz invariant? Does the possibility of superluminal information transfer compromise special relativity, even though the possibility of superluminal signalling and communication, by way of instantaneous, i.e., nonlocal transfers, is fully denied? In other words, is it inevitable that causal paradoxes are generated automatically—as a function of nonlocal quantum information transfers—even in the complete absence of experimenter agents and of their laboratory devices, i.e., if nature is left to herself ? The subsequent discussion is intended to provide an initial orientation for such work

Summary

Introduction

Bell’s theorem proved that no quantum theory based on the joint assumptions of “causality and locality” can successfully reproduce the predictions that are yielded by orthodox quantum mechanics [1]. As we will discuss at length further below, Bell here refers to the special, and still incompletely understood, ‘role of us’—human observers and of epistemic agents in general—both in the performance of quantum-based experiments and in possible definitions of the non-signalling constraint (e.g., [4]). The impossibility to signal by way of superluminal influences Bell took to be the central issue for any explanatory, causal approaches to quantum mechanics [7]: “For me this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation and fundamental relativity.”. The present work introduces a conceptual framework for defining, in a technically consistent manner, the difference between signalling, information transfer, and message communication These concepts are sometimes used interchangeably and often without clear definition in the literature on quantum foundations. We will present an overview of the contrasting uses of the non-signalling theorem in quantum mechanics, employing as a historical reference the two interpretations used by John Bell

The Two Interpretations by John Bell of the Non-signalling Theorem

Defining the Epistemic Agent

Two Sub-theorems Represent an Effective Non-signalling Theorem

Discussion

Conclusions