Supersonic quantum communication

TL;DR

This paper demonstrates that in translationally invariant bosonic lattice models, excitations can accelerate and transmit information faster than the traditional finite speed of sound, challenging existing Lieb-Robinson bounds.

Contribution

It proves that bosonic models can exhibit superluminal-like propagation, unlike spin models, impacting understanding of non-equilibrium dynamics and simulation complexity.

Findings

Excitations can accelerate beyond finite speed of sound.

Fast information transmission is possible in bosonic models.

Non-equilibrium dynamics lead to rapid entanglement growth.

Abstract

When locally exciting a quantum lattice model, the excitation will propagate through the lattice. The effect is responsible for a wealth of non-equilibrium phenomena, and has been exploited to transmit quantum information through spin chains. It is a commonly expressed belief that for local Hamiltonians, any such propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson theorem states that in spin models, all effects caused by a perturbation are limited to a causal cone defined by a constant speed, up to exponentially small corrections. In this work we show that for translationally invariant bosonic models with nearest-neighbor interactions, this belief is incorrect: We prove that one can encounter excitations which accelerate under the natural dynamics of the lattice and allow for reliable transmission of information faster than any finite speed of sound. The effect is only limited by the model's range of validity (eventually by relativity). It also implies that in non-equilibrium dynamics of strongly correlated bosonic models far-away regions may become quickly entangled, suggesting that their simulation may be much harder than that of spin chains even in the low energy sector.