In this work, we explore the space of quantum states composed of $N$ particles. To investigate entanglement resistant to particle 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 any 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 $N$-particle states with the desired property of entanglement resistance to particle loss.

• Received 11 September 2019

DOI:https://doi.org/10.1103/PhysRevA.100.062329