Simulation of Gaussian channels via teleportation and error correction of Gaussian states

TL;DR

This paper develops a method to simulate Gaussian channels using physically feasible resource states with finite energy and entanglement, optimizing their properties and extending error correction protocols to thermal loss channels.

Contribution

It derives the set of optimal finite-resource states for simulating Gaussian channels via teleportation, and generalizes error correction to thermal loss channels.

Findings

Optimal resource states are pure and have entanglement equal to the Choi-state.

The same entanglement suffices to simulate channels with equivalent decoherence.

More entanglement can simulate less decohering channels.

Abstract

Gaussian channels are the typical way to model the decoherence introduced by the environment in continuous-variable quantum states. It is known that those channels can be simulated by a teleportation protocol using as a resource state either a maximally entangled state passing through the same channel, i.e., the Choi-state, or a state that is entangled at least as much as the Choi-state. Since the construction of the Choi-state requires infinite mean energy and entanglement, i.e. it is unphysical, we derive instead every physical state able to simulate a given channel through teleportation with finite resources, and we further find the optimal ones, i.e., the resource states that require the minimum energy and entanglement. We show that the optimal resource states are pure and equally entangled to the Choi-state as measured by the entanglement of formation. We also show that the same amount of entanglement is enough to simulate an equally decohering channel, while even more entanglement can simulate less decohering channels. We, finally, use that fact to generalize a previously known error correction protocol by making it able to correct noise coming not only from pure loss but from thermal loss channels as well.