Quantum macroscopicity versus distillation of macroscopic superpositions

TL;DR

This paper introduces a method to quantify macroscopic entanglement through distillation of GHZ states and compares it with quantum Fisher information, revealing robustness differences in cluster states based on dimensionality.

Contribution

It proposes a new measure of macroscopic entanglement via GHZ state distillation and analyzes its relation to quantum macroscopicity, highlighting robustness in higher-dimensional cluster states.

Findings

Cluster states and Kitaev surface code states are not macroscopically quantum.

Higher-dimensional cluster states are robust to perturbations during distillation.

One-dimensional cluster states are not robust in distillation protocols.

Abstract

We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional cluster states are not distilled robustly but higher-dimensional cluster states are.