Geometric Quantum State Estimation

Fabio Anza and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

ABSTRACT: Density matrices capture all of a quantum system's statistics accessible through projective and positive operator-valued measurements. They do not completely determine its state, however, as they neglect the physical realization of ensembles. Fortunately, the concept of geometric quantum state does properly describe physical ensembles. Here, given knowledge of a density matrix, possibly arising from a tomography protocol, we show how to estimate the geometric quantum state using a maximum entropy principle based on a geometrically-appropriate entropy.

Fabio Anza and James P. Crutchfield, “Geometric Quantum State Estimation”, (2020).
[pdf]. [quant-phys].