Maximum Geometric Quantum Entropy

ABSTRACT: Density matrices capture all of a quantum system's statistics accessible through projective and positive operator-valued measurements. They do not specify how system statistics are created, however, as they neglect the physical realization of ensembles. Geometric quantum states—probability distributions of the system state conditioned on the environment state—were developed to track ensembles efficiently, using geometric quantum mechanics. Here, given knowledge of a density matrix, we show how to estimate the geometric quantum state using a maximum entropy principle based on a geometrically-appropriate quantum entropy.