Reachability Constraints and Monotones for Quantum-State Texture

arXiv:2611.09230v1 Announce Type: new Abstract: How a quantum resource can be quantified depends on which operations are free. Yet two proposed quantifiers of quantum state texture can increase under free operations: the Wigner-Yanase-Dyson skew information relative to the unique textureless state and the squared Hilbert-Schmidt distance from that state. We show reachability from every state orthogonal to the textureless state, whether pure or mixed: each can be freely transformed into any other state. Therefore, every texture monotone must assign the same maximal value to all such states, a requirement that neither candidate satisfies.