Entanglement of assistance in three-qubit systems

TL;DR

This paper investigates how much entanglement can be preserved or lost in three-qubit systems when a helper party performs local measurements, revealing conditions for lossless decoupling across different entanglement measures.

Contribution

It characterizes the conditions under which lossless decoupling is possible in three-qubit states, especially highlighting differences across various entanglement measures.

Findings

Lossless decoupling always possible with Bell state probability measure.

Lossless decoupling only for specific states with concurrence or entropy measures.

Complete characterization of states allowing lossless decoupling for most measures.

Abstract

The entanglement of assistance quantifies the amount of entanglement that can be concentrated among a group of spatially-separated parties using the assistance of some auxiliary system. In this paper we study the entanglement of assistance in the simplest scenario of three qubits. We consider how much entanglement is lost when the helper party becomes uncoupled by local measurement and classical communication. For three-qubit pure states, it is found that lossless decoupling is always possible when entanglement is quantified by the maximum probability of locally generating a Bell state. However, with respect to most other entanglement measures, such as concurrence and entanglement entropy, a lossless decoupling of the helper is possible only for a special family of states that we fully characterize.