Residual effect on the robustness of multiqubit entanglement

TL;DR

This paper explores how entanglement influences the robustness of multiqubit systems against depolarization noise, revealing a residual effect in three-qubit states and complex behaviors in larger systems.

Contribution

It uncovers the residual effects of entanglement on robustness in multiqubit states, especially highlighting differences in three-qubit and larger systems.

Findings

Robustness of two-qubit pure states depends solely on entanglement.

Three-qubit superpositions show a residual effect with robustness splitting.

Robustness in larger systems exhibits complex, non-uniform behavior.

Abstract

We investigate the relation between the entanglement and the robustness of a multipartite system to a depolarization noise. We find that the robustness of a two-qubit system in an arbitrary pure state depends completely on its entanglement. However, this is not always true in a three-qubit system. There is a residual effect on the robustness of a three-qubit system in an arbitrary superposition of Greenberger-Horne-Zeilinger state and W state. Its entanglement determines the trend of its robustness. However, there is a splitting on its robustness under the same entanglement. Its robustness not only has the same periodicity as its three-tangle but also alters with its three-tangle synchronously. There is also a splitting on the robustness of an $n$-qubit ($n>3$) system although it is more complicated.