Quantum network-entanglement measures
arXiv:2311.13945 · doi:10.22331/q-2025-05-06-1736
Abstract
Quantum networks are of high interest nowadays and a quantum internet has been long envisioned. Network-entanglement adapts the notion of entanglement to the network scenario and network-entangled states are considered to be a resource to overcome the limitations of a given network structure. In this work, we introduce measures of quantum network-entanglement that are well-defined within the general framework of quantum resource theories, which at the same time have a clear operational interpretation characterizing the extra resources necessary to prepare a targeted quantum state within a given network. In particular, we define the network communication cost and the network round complexity, which turn out to be intimately related to graph-theoretic parameters. We also provide methods to estimate these measures by introducing novel witnesses of network-entanglement.
7+21 pages, 9 figures
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