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