Entanglement, intractability and no-signaling

TL;DR

This paper explores the connection between no-signaling, computational complexity, and hypothetical superluminal gates, proposing an experiment that could demonstrate such gates and challenging standard quantum observables.

Contribution

It introduces the concept of polynomial superluminal gates, links them to no-signaling and complexity theory, and proposes a feasible experiment to detect their effects.

Findings

A modified quantum optical experiment can potentially demonstrate superluminal gates.

Standard quantum observables may not fully describe certain quantum optical quantities.

Counter-claims against the experiment's implications are addressed and invalidated.

Abstract

We consider the problem of deriving the no-signaling condition from the assumption that, as seen from a complexity theoretic perspective, the universe is not an exponential place. A fact that disallows such a derivation is the existence of {\em polynomial superluminal} gates, hypothetical primitive operations that enable superluminal signaling but not the efficient solution of intractable problems. It therefore follows, if this assumption is a basic principle of physics, either that it must be supplemented with additional assumptions to prohibit such gates, or, improbably, that no-signaling is not a universal condition. Yet, a gate of this kind is possibly implicit, though not recognized as such, in a decade-old quantum optical experiment involving position-momentum entangled photons. Here we describe a feasible modified version of the experiment that appears to explicitly demonstrate the action of this gate. Some obvious counter-claims are shown to be invalid. We believe that the unexpected possibility of polynomial superluminal operations arises because some practically measured quantum optical quantities are not describable as standard quantum mechanical observables.