Characterization of rank-deficient models with finite-copy Holevo-bound closure

Characterize which rank-deficient quantum estimation models admit exact finite-copy attainment of the Holevo bound, and determine how this property can be realized in physically motivated sensing models.

Background

The paper demonstrates finite-copy closure using a specifically constructed three-parameter rank-two model and shows that full-rank models cannot exhibit the same phenomenon under a strict single-copy gap. The construction therefore establishes existence but does not provide a general classification of rank-deficient models with this property.

The authors explicitly identify the broader classification of such models and their realization in physically motivated sensing scenarios as unresolved. This problem concerns both the structural characterization of finite-copy closure and its relevance to experimentally meaningful quantum sensing systems.