Symmetric extendibility for a class of qudit states

TL;DR

This paper develops criteria to determine symmetric extendibility in certain two-qudit quantum states, aiding quantum cryptography by identifying states suitable for one-way entanglement purification.

Contribution

It provides the first complete criteria for symmetric extendibility in a specific two-parameter family of two-qudit states, including isotropic states.

Findings

Criteria for symmetric extendibility derived for subclasses of two-qudit states

Complete solution for a two-parameter family of states including isotropic states

Facilitates identification of states suitable for one-way quantum entanglement purification

Abstract

The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means of entanglement purification with one-way classical communication only. Unfortunately, at present there exists no simple general criterion to decide whether a state possesses a symmetric extension or not. In this article we derive criteria for symmetric extendibility within subclasses of all two-qudit states. Using these criteria, we can completely solve the problem for a two-parameter family of two-qudit states, which includes the isotropic states as a subclass.