Multiparty entanglement routing in quantum networks
Vaisakh Mannalath, Anirban Pathak
Abstract
Distributing entanglement among multiple users is a fundamental problem in quantum networks, requiring an efficient solution. In this work, a protocol is proposed for extracting maximally entangled ($|{\text{GHZ}}_{n}\ensuremath{\rangle}$) states for any number of parties in a quantum network. It is based on the graph-state formalism and requires minimal assumptions on the network state. The protocol only requires local measurements at the network nodes and just a single-qubit memory per user. Existing protocols on bipartite entanglement routing are also improved for specific nearest-neighbor network architectures. To this end, the concept of majorization is utilized to establish a hierarchy among different paths in a network based on their efficacy. This approach utilizes the symmetry of the underlying graph state to obtain better-performing algorithms.