Enumerating all bilocal Clifford distillation protocols through symmetry reduction
Sarah Jansen (Student TU Delft, Korteweg-de Vries Institute for Mathematics)
K.D. Goodenough (TU Delft - QID/Wehner Group, TU Delft - QuTech Advanced Research Centre)
Sébastian de Bone (QuSoft, TU Delft - QuTech Advanced Research Centre, TU Delft - QID/Elkouss Group)
DC Gijswijt (TU Delft - Discrete Mathematics and Optimization)
David Elkouss Coronas (Okinawa Institute of Science and Technology Graduate University, TU Delft - Quantum Information and Software, TU Delft - QuTech Advanced Research Centre)
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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.
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