Bounds on the Speedup in Quantum signalling

TL;DR

This paper investigates the limits of quantum signalling speedup, showing that quantum dynamics cannot significantly surpass classical bounds over multiple steps, despite initial advantages in local change detection.

Contribution

It establishes bounds on quantum speedup in signalling, demonstrating that quantum advantages do not grow asymptotically over classical limits.

Findings

Quantum dynamics can detect local changes farther after one step.

No asymptotic increase in propagation speed in quantum signalling.

Quantum speedup is limited to a constant fringe over many steps.

Abstract

Given a discrete reversible dynamics, we can define a quantum dynamics, which acts on basis states like the classical one, but also allows for superpositions of them. It is a curious fact that in the quantum version, local changes in the initial state, after a single dynamical step, can sometimes can be detected much farther away than classically. Here we show that this effect is no use for generating faster signals. In a run of many steps the quantum propagation neighborhood can only increase by a constant fringe, so there is no asymptotic increase in speed.