An Information-Theoretic Principle for Optimal Quantum Encoding: Tight Frames and Equiangular Ensembles
The paper investigates how to best encode classical data for quantum statistical inference by using information theory. It proves that maximizing 'maximal quantum leakage' is the universal measure for optimal encoding, leading to strategies based on pure states or Equiangular Tight Frames (ETFs). This means maximizing this leakage ensures the best possible accuracy for any quantum task, regardless of the specific problem.