Graph state generation with noisy mirror-inverting spin chains

TL;DR

This paper analyzes how different types of noise affect the ability of a mirror-inverting spin chain to generate graph states, focusing on entanglement preservation and fidelity in noisy conditions.

Contribution

It provides a detailed numerical analysis of noise effects on a spin chain used as an entanglement bus, identifying critical noise levels for entanglement breaking.

Findings

Local decay and dephasing do not cause entanglement breaking.

Thermal and depolarizing noise can cause entanglement breaking at critical lengths and noise levels.

Noise constraints are tight for constructing multi-qubit graph states with the spin chain.

Abstract

We investigate the influence of noise on a graph state generation scheme which exploits a mirror inverting spin chain. Within this scheme the spin chain is used repeatedly as an entanglement bus (EB) to create multi-partite entanglement. The noise model we consider comprises of each spin of this EB being exposed to independent local noise which degrades the capabilities of the EB. Here we concentrate on quantifying its performance as a single-qubit channel and as a mediator of a two-qubit entangling gate, since these are basic operations necessary for graph state generation using the EB. In particular, for the single-qubit case we numerically calculate the average channel fidelity and whether the channel becomes entanglement breaking, i.e., expunges any entanglement the transferred qubit may have with other external qubits. We find that neither local decay nor dephasing noise cause entanglement breaking. This is in contrast to local thermal and depolarizing noise where we determine a critical length and critical noise coupling, respectively, at which entanglement breaking occurs. The critical noise coupling for local depolarizing noise is found to exhibit a power-law dependence on the chain length. For two qubits we similarly compute the average gate fidelity and whether the ability for this gate to create entanglement is maintained. The concatenation of these noisy gates for the construction of a five qubit linear cluster state and a Greenberger-Horne-Zeilinger state indicates that the level of noise that can be tolerated for graph state generation is tightly constrained.