Operational resource theory of quantum learnability

Develop an operational resource theory of learnability that organizes the spectral, metrological, and measurement-accessible ingredients of quantum learning into a common framework extendable to variational, kernel-based, and other quantum-learning architectures.

Background

The paper relates computationally useful quantum dynamics to subsystem spectral nonflatness, quantum Fisher information, and the accessibility of response through restricted measurements. It argues that these ingredients provide necessary conditions for effective information processing but do not by themselves constitute a complete resource theory.

The unresolved problem is to organize these ingredients into an operational framework with a common notion of resource and applicability across multiple quantum-learning paradigms, including variational and kernel-based architectures. Such a theory could also clarify when quantum advantage arises alongside classical intractability.