Cut-resistant links and multipartite entanglement resistant to particle loss

TL;DR

This paper introduces the concept of m-resistant quantum states that maintain entanglement despite particle loss, drawing an analogy to topological links, and provides constructive solutions for such states.

Contribution

It defines m-resistant states in quantum entanglement and offers a constructive method to create states resistant to particle loss, inspired by topological link design.

Findings

Defined m-resistant entangled states.

Established analogy with topological links.

Provided constructive solutions for resistant states.

Abstract

In this work, we explore the space of quantum states composed of $N$ particles. To investigate the entanglement resistant to particles loss, we introduce the notion of $m$-resistant states. A quantum state is $m$-resistant if it remains entangled after losing an arbitrary subset of m particles, but becomes separable after losing a number of particles larger than $m$. We establish an analogy to the problem of designing a topological link consisting of $N$ rings such that, after cutting any $(m + 1)$ of them, the remaining rings become disconnected. We present a constructive solution to this problem, which allows us to exhibit several distinguished $N$-particles states with the desired property of entanglement resistance to a particle loss.