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.

arXiv comment14 pages, 12 figures

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• Entanglement in highly symmetric multipartite quantum states
• Genuine Multipartite Entanglement induced by a Thermal Acoustic Reservoir
• Correlations for subsets of particles in symmetric states: what photons are doing within a beam of light when the rest are ignored
• Borromean states in discrete-time quantum walks
• Absolutely maximally entangled pure states of multipartite quantum systems
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
• Robust Multipartite Entanglement Without Entanglement Breaking