Establish separability preservation for general quantum-switch conditional maps

Establish whether the conditional maps generated by a quantum switch with general local intermediate unitaries and general noisy channels preserve separability across the certified bipartition, thereby determining when entanglement detected after postselection certifies entanglement of the input.

Background

The paper proves separability preservation for the Pauli and Weyl constructions and for the amplitude-damping example with an identity intermediate operation because the conditional maps admit separable Kraus decompositions. For arbitrary local intermediate unitaries and arbitrary channels, the coherent sums of the two causal-order Kraus operators need not remain product operators, so the required separability-preserving property is not automatic.

This unresolved issue limits the interpretation of the reported numerical scans: for general local unitaries and general channels, the authors compare output-state negativities rather than claiming certified input entanglement. Establishing separability preservation, or identifying precise sufficient conditions for it, would extend the entanglement-certification guarantees beyond the special noise and unitary families analyzed in the paper.