{
  "id": "1910.03315",
  "version": "v1",
  "published": "2019-10-08T10:15:40.000Z",
  "updated": "2019-10-08T10:15:40.000Z",
  "title": "Quantum linear network coding for entanglement distribution in restricted architectures",
  "authors": [
    "Niel de Beaudrap",
    "Steven Herbert"
  ],
  "comment": "30 pages, 11 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In this paper we propose a technique for distributing entanglement in architectures in which interactions between pairs of qubits are constrained to a fixed network $G$. This allows for two-qubit operations to be performed between qubits which are remote from each other in $G$, through gate teleportation. We demonstrate how adapting \\emph{quantum linear network coding} to this problem of entanglement distribution in a network of qubits can be used to solve the problem of distributing Bell states and GHZ states in parallel, when bottlenecks in $G$ would otherwise force such entangled states to be distributed sequentially. In particular, we show that by reduction to classical network coding protocols for the $k$-pairs problem or multiple multicast problem in a fixed network $G$, one can distribute entanglement between the transmitters and receivers with a Clifford circuit whose quantum depth is some (typically small and easily computed) constant, which does not depend on the size of $G$, how remote the transmitters and receivers are, or the number of transmitters and receivers. These results also generalise straightforwardly to qudits of any prime dimension. We demonstrate our results using a specialised formalism, distinct from and more efficient than the stabiliser formalism, which is likely to be helpful to reason about and prototype such quantum linear network coding circuits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-08T10:15:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entanglement distribution",
      "restricted architectures",
      "quantum linear network coding circuits",
      "fixed network",
      "transmitters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}