No-signaling, intractability and entanglement

TL;DR

This paper explores the connection between no-signaling, computational complexity, and hypothetical superluminal gates, proposing an experiment to demonstrate such gates and discussing implications for physics and quantum mechanics.

Contribution

It introduces the concept of polynomial superluminal gates and suggests a feasible experiment to demonstrate their existence, challenging assumptions about no-signaling.

Findings

Proposes a modified experiment to demonstrate superluminal gates.

Shows that some quantum optical quantities may not be standard observables.

Discusses implications for the universality of no-signaling.

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 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.