Eliminating the logarithmic input-dimension dependence in general strong converse bounds for identification

Develop a strong converse upper bound on the classical identification capacity for arbitrary finite-dimensional quantum channels that removes the additive dependence on log|A| (the logarithm of the input Hilbert space dimension) present in existing bounds for general channels.

Background

For general quantum channels, the authors replace the strong converse quantum capacity with the classical capacity in existing soft-covering-based bounds, obtaining an upper bound of log|A| + C(N).

They note, however, that unlike their depolarizing-channel-specific approach that avoids a dimension term, they currently cannot eliminate the log|A| term in the general setting, and explicitly flag this as an unresolved issue.

References

As noted in Section 3, we do not presently know how to eliminate the logarithmic dependence on the input dimension.

— Strong converse bounds on the classical identification capacity of the qubit depolarizing channel  (2603.29987 - Ye et al., 31 Mar 2026) in Section 6: For general channels — A strong converse bound for the unrestricted identification capacity in terms of the classical capacity