An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles

What the math gives to ML

The paper provides a principled construction of maximally symmetric codebooks: unit-norm vectors whose frame operator is isotropic and whose pairwise overlaps attain the Welch bound. This structure transfers directly to neural representation learning, where classifier prototypes or embedding codewords can otherwise collapse into anisotropic, redundant directions. A fixed or softly constrained equiangular tight-frame output head can make class geometry uniform, improve conditioning of the final logits, and provide a task-independent anti-collapse prior. The most practical experiment is to compare a standard learned normalized classifier against an ETF-initialized or fixed head and against a learnable head with tight-frame and Welch-coherence penalties.