Extension to post-selection and trace-nonincreasing operations

Extend the bipartite relative-entropy formulation and candidate-and-certificate algorithm for quantum key distribution key-rate estimation to the general case involving post-selections and trace-nonincreasing operations.

Background

The paper formulates the quantum key-distribution key-rate problem as the minimization of a relative entropy over a feasible set of bipartite quantum states subject to affine measurement constraints. After support compression, the method applies to completely positive trace-preserving preprocessing and pinching maps, enabling efficient Gibbs-state iterations and spectral certificates.

The authors explicitly note that this formulation does not yet cover the general setting involving post-selections and therefore trace-nonincreasing operations. Extending the framework to that setting is left unresolved, despite the practical relevance of post-selection in quantum key-distribution protocols.

References

For now this setting already covers a lot of qkd cases, it does not hold yet for the general case involving post-selections and thus trace-nonincreasing operations. We leave that extension to future work.

— Efficient Computation of QKD Key Rates without Semidefinite Programming  (2608.23285 - Temesi et al., 24 Aug 2026) in Section 2, Methods, subsection “Formulation as bipartite relative entropy optimization”