Deterministic transformations between arbitrary mixed states

Derive necessary and sufficient conditions for deterministic transformations between arbitrary mixed quantum states under texture-free operations, extending the complete qubit characterization to general mixed states.

Background

The paper establishes deterministic state-conversion criteria for arbitrary qubit states under texture-free operations, expressed in terms of the Bloch vectors of the initial and target states. However, it does not provide a corresponding characterization for arbitrary mixed states in higher-dimensional systems or, more generally, for arbitrary mixed-state pairs. The authors identify this unresolved characterization as an important open problem for the resource theory of quantum-state texture.