BAYESIAN-INFERENCE FOR COMPLEX AND QUATERNIONIC 2-LEVEL QUANTUM-SYSTEMS

Jeffreys' approach for generating reparameterization-invariant prior d istributions is applied to the three-dimensional convex set of complex two-level quantum systems. For this purpose, such systems are identif ied with bivariate complex normal distributions over the vectors of tw o-dimensional complex Hilbert space. The trivariate prior obtained is improper or non-normalizable over the convex set. However, its three b ivariate marginals are - through a limiting procedure - normalizable t o probability distributions and are, consequently, suitable for the Ba yesian inference of two-level systems. Analogous results hold for the five-dimensional convex set of quaternionic two-level systems. The com plex univariate and quaternionic trivariate marginals of the improper priors are uniform distributions. The bivariate marginals in the two c ases are opposite in character.