Cut-resistant links and multipartite entanglement resistant to particle loss

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.