Calculating Concentratable Entanglement in Graph States

TL;DR

This paper introduces a stabilizer-based method to compute the purity and Concentratable Entanglement of graph states, enabling efficient analysis of entanglement properties in quantum information applications.

Contribution

It presents a novel approach to calculate Concentratable Entanglement directly from stabilizer generators, applicable to various important graph states.

Findings

Method effectively computes purity of reduced states.

Identifies states with maximum and minimum Concentratable Entanglement.

Demonstrates applicability to quantum repeater states.

Abstract

We propose a method to calculate the purity of reduced states of graph states entirely within the stabilizer formalism, using only the stabilizer generators for a given state. We apply this method to find the Concentratable Entanglement of graph states, with examples including a single qubit within any graph state, states proposed for use in quantum repeaters and states that maximise and minimise the overall Concentratable Entanglement.