Correlations and energy in mediated dynamics

TL;DR

This paper investigates the minimal time and energy costs for entangling two quantum systems either directly or via a mediator, revealing that initial correlations in the mediator can match direct interaction speed without extra energy.

Contribution

It demonstrates that mediated entanglement can be as fast as direct entanglement if the mediator is initially correlated, highlighting the role of correlations in energy efficiency.

Findings

Direct interactions are fastest for entanglement.

Mediator with initial correlations can match direct interaction speed.

Correlations can be classical and remain during entanglement.

Abstract

The minimum time required for a quantum system to evolve to a distinguishable state is set by the quantum speed limit, and consequently influences the change of quantum correlations and other physical properties. Here we study the time required to maximally entangle two principal systems interacting either directly or via a mediating ancillary system, under the same energy constraints. The direct interactions are proved to provide the fastest way to entangle the principal systems, but it turns out that there exist mediated dynamics that are just as fast. We show that this can only happen if the mediator is initially correlated with the principal systems. These correlations can be fully classical and can remain classical during the entangling process. The final message is that correlations save energy: one has to supply extra energy if maximal entanglement across the principal systems is to be obtained as fast as with an initially correlated mediator.