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.


Jansen, S, Goodenough, K, de Bone, S.W, Gijswijt, D, & Elkouss, D. (2022). Enumerating all bilocal Clifford distillation protocols through symmetry reduction. Quantum, 6, 715.1–715.25. doi:10.22331/Q-2022-05-19-715