New constructions of multipartite entanglement resistant to particle loss

TL;DR

This paper introduces two new methods for constructing multipartite entangled states that remain entangled despite the loss of a certain number of particles, advancing understanding of entanglement robustness.

Contribution

It provides two general constructions of m-resistant pure states, one using mixtures of Dicke states and another based on classical error correcting codes.

Findings

Constructed strong (N - k)-resistant pure N-qubit states with k=4 or 5.

Developed new m-resistant qudit states for certain m < N/2.

Validated the existence of m-resistant states for various parameters.

Abstract

An entangled state is called m-resistant if it remains entangled after losing an arbitrary subset of mparticles but becomes fully separable after losing any number of particles larger than m. Quinta et al. [Phys. Rev. A (2019)] conjectured that for any N-particle systems, there always exists an m-resistant pure state. In this paper, we give two general constructions of m-resistant pure states. One is from the mixtures of Dicke states, which provides strong (N - k)-resistant pure N-qubit states with k = 4 or 5. The other is from classical error correcting codes, which provides new m-resistant qudit states for certain m < N/2.