cff-version: 1.2.0
abstract: "Entanglement distillation is an essential building block in quantum communication protocols. Here, we study the class of near-term implementable distillation protocols that use bilocal Clifford operations followed by a single round of communication.  We introduce tools to enumerate and optimise over all protocols for up to n=5 (not necessarily equal) Bell-diagonal states using a commodity desktop computer. Furthermore, by exploiting the symmetries of the input states, we find all protocols for up to n=8 copies of a Werner state. For the latter case, we present circuits that achieve the highest fidelity with perfect operations and no decoherence. These circuits have modest depth and number of two-qubit gates. Our results are based on a correspondence between distillation protocols and double cosets of the symplectic group, and improve on previously known protocols."
authors:
  - family-names: de Bone
    given-names: Sebastian
    orcid: "https://orcid.org/0000-0001-6423-8761"
  - family-names: Goodenough
    given-names: Kenneth
  - family-names: Elkouss
    given-names: David
    orcid: "https://orcid.org/0000-0003-2023-2768"
  - family-names: Gijswijt
    given-names: Dion
    orcid: "https://orcid.org/0000-0003-0734-4511"
  - family-names: Jansen
    given-names: Sarah
title: "Data/software underlying the publication: Enumerating all bilocal Clifford distillation protocols through symmetry reduction"
keywords:
version: 1
identifiers:
  - type: doi
    value: 10.4121/15082515.v1
license: CC0
date-released: 2021-09-22