Optimal numerical hierarchy for one-sided DIQKD optimization

Determine which of the NPA-AC hierarchy with matrix-algebra constraints and the NPA-MP hierarchy with matrix-valued polynomials is best suited to each class of one-sided device-independent quantum key distribution optimization problem.

Background

The paper introduces and compares two numerical approaches: NPA-AC, which incorporates finite-dimensionality through matrix-algebra constraints, and NPA-MP, which uses matrix-valued polynomials. Their observed performance is problem-dependent: NPA-AC is slightly faster in the reported calculations, whereas NPA-MP uses less memory. The authors therefore identify a broader comparative question concerning the circumstances in which either method is preferable.

References

Another open question is which numerical method is best suited for which type of problem: In our numerical calculations, we observed that the NPA-AC hierarchy is slightly faster than the NPA-MP hierarchy (as shown in Table~\ref{tab:runtime_comparison}), whereas the latter uses less memory.

— Computing key rates for one-sided device-independent quantum key distribution  (2608.25915 - Bluhm et al., 26 Aug 2026) in Section "Discussion and outlook"