Superluminal signalling and chaos in nonlinear quantum dynamics

TL;DR

This paper examines the implications of nonlinear quantum dynamics on superluminal signalling, revealing that chaos and specific conditions can allow or prevent faster-than-light communication, challenging existing no-go theorems.

Contribution

It analyzes the Gisin no-go theorem in the context of recent developments and introduces a class of chaotic nonlinear quantum dynamics that can enable superluminal signalling under certain conditions.

Findings

Nonlinear quantum dynamics can exhibit chaotic behavior.

Superluminal signalling is possible with certain nonlinear dynamics.

Relaxing the no-restriction hypothesis can prevent superluminal communication.

Abstract

Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin proved a powerful no-go theorem, according to which nonlinear quantum dynamics would lead to superluminal signalling, violating Einstein's causality. Here we analyse the theorem from the perspective of recent developments. First, we observe that it harmonises with the no-restriction hypothesis from General Probabilistic Theories. Second, we note that it requires a suitable synchronisation of Alice's and Bob's clocks and actions. Next, we argue that it does not automatically exclude the possibility of global nonlinear quantum dynamics on a tensor product Hilbert space. Consequently, we investigate a class of such dynamics inspired by discrete analogues of nonlinear Schr\"odinger equations. We show that, in general, they exhibit a chaotic character. In this context we inspect whether superluminal signalling can be avoided by relaxing the no-restriction hypothesis. We study three possible communication protocols involving either local measurements or modifications of a local Hamiltonian. We conclude that, in general, in all three cases, two spacelike separated parties can effectuate statistical superluminal information transfer. Nevertheless, we show an example of a nonlocal nonlinear quantum dynamics, which does not allow for it, provided that we relax the no-restriction hypothesis.