Enumerating all bilocal Clifford distillation protocols through symmetry reduction

• URL: http://arxiv.org/abs/2103.03669v5
• Date: Tue, 17 May 2022 11:14:07 GMT
• Title: Enumerating all bilocal Clifford distillation protocols through symmetry reduction
• Authors: Sarah Jansen, Kenneth Goodenough, S\'ebastian de Bone, Dion Gijswijt, David Elkouss
• Abstract summary: Entanglement distillation is an essential building block in quantum communication protocols. We study the class of near-term implementable distillation protocols that use bilocal Clifford operations. We present circuits that achieve the highest fidelity with perfect operations and no decoherence.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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