Enumerating all bilocal Clifford distillation protocols through symmetry reduction

Enumerating all bilocal Clifford distillation protocols through symmetry reduction

Jansen, Sarah (Korteweg-de Vries Institute for Mathematics; Student TU Delft)
Goodenough, K.D. (TU Delft QID/Wehner Group; TU Delft QuTech Advanced Research Centre)
de Bone, S.W. (TU Delft QID/Elkouss Group; TU Delft QuTech Advanced Research Centre; QuSoft)
Gijswijt, Dion (TU Delft Discrete Mathematics and Optimization)
Elkouss Coronas, D. (TU Delft Quantum Information and Software; TU Delft QuTech Advanced Research Centre; Okinawa Institute of Science and Technology Graduate University)

2022

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.

http://resolver.tudelft.nl/uuid:7f94f321-b94d-40d1-a0d2-923b9f60f875

https://doi.org/10.22331/Q-2022-05-19-715

2521-327X

QUANTUM, 6

Institutional Repository

journal article

© 2022 Sarah Jansen, K.D. Goodenough, S.W. de Bone, Dion Gijswijt, D. Elkouss Coronas