Entanglement in pure and thermal cluster states

TL;DR

This paper develops a method to identify the closest separable states to cluster states, enabling quantification of entanglement in both pure and noisy thermal states, with implications for quantum computation.

Contribution

It introduces a novel approach to find the closest separable states for cluster states, applicable to noisy states and providing operational insights.

Findings

Reproduces known results for pure cluster states

Extends method to thermal (noisy) cluster states

Identifies critical temperature for classical correlation transition

Abstract

We present a closest separable state to cluster states. We start by considering linear cluster chains and extend our method to cluster states that can be used as a universal resource in quantum computation. We reproduce known results for pure cluster states and show how our method can be used in quantifying entanglement in noisy cluster states. Operational meaning is given to our method that clearly demonstrates how these closest separable states can be constructed from two-qubit clusters in the case of pure states. We also discuss the issue of finding the critical temperature at which the cluster state becomes only classically correlated and the importance of this temperature to our method.