Open-system dynamics of graph-state entanglement

TL;DR

This paper develops methods to analyze how entanglement in graph states evolves under decoherence, providing exact bounds for Pauli channels and insights into the robustness of these states based on their connectivity.

Contribution

It introduces a novel approach to bound and exactly determine entanglement decay in graph states under noise, applicable to any convex entanglement measure.

Findings

Exact entanglement evolution for Pauli channels

Lower bounds for arbitrary states via local depolarization

Robustness of graph states depends on connectivity

Abstract

We consider graph states of arbitrary number of particles undergoing generic decoherence. We present methods to obtain lower and upper bounds for the system's entanglement in terms of that of considerably smaller subsystems. For an important class of noisy channels, namely the Pauli maps, these bounds coincide and thus provide the exact analytical expression for the entanglement evolution. All the results apply also to (mixed) graph-diagonal states, and hold true for any convex entanglement monotone. Since any state can be locally depolarized to some graph-diagonal state, our method provides a lower bound for the entanglement decay of any arbitrary state. Finally, this formalism also allows for the direct identification of the robustness under size scaling of graph states in the presence of decoherence, merely by inspection of their connectivities.