Data/software underlying the publication: Enumerating all bilocal Clifford distillation protocols through symmetry reduction
softwareposted on 2021-09-22, 11:19 authored by Sébastian de BoneSébastian de Bone, Kenneth GoodenoughKenneth Goodenough, David ElkoussDavid Elkouss, Dion Gijswijt, Sarah Jansen
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.