Entanglement robustness against particle loss in multiqubit systems

TL;DR

This paper investigates the robustness of multiqubit entangled states against particle loss, identifying fragile states and analyzing symmetric states within the SLOCC classification framework.

Contribution

It exhaustively characterizes all entangled states that are fragile to single-qubit loss and analyzes the robustness of symmetric states in the context of SLOCC classification.

Findings

Identified all fragile entangled states under single-qubit loss.

Analyzed entanglement robustness of symmetric states.

Placed robustness properties within SLOCC classification.

Abstract

When some of the parties of a multipartite entangled pure state are lost, the question arises whether the residual mixed state is also entangled, in which case the initial entangled pure state is said to be robust against particle loss. In this paper, we investigate this entanglement robustness for $N$-qubit pure states. We identify exhaustively all entangled states that are fragile, i.e., not robust, with respect to the loss of any single qubit of the system. We also study the entanglement robustness properties of symmetric states and put these properties in the perspective of the classification of states with respect to stochastic local operations assisted with classic communication (SLOCC classification).