Geometrical structures for classical and quantum probability spaces

Geometrical Statistics — Classical and Quantum

This is a review of the ideas behind the Fisher–Rao metric on classical probability distributions, and how they generalize to metrics on density matrices. As is well known, the unique Fisher–Rao metric then becomes a large family of monotone metrics. Finally I focus on the Bures–Uhlmann metric, and discuss a recent result that connects the geometric operator mean to a geodesic billiard on the s...

Classical and Quantum Probability

We follow the development of probability theory from the beginning of the last century, emphasising that quantum theory is really a generalisation of this theory. The great achievements of probability theory, such as the theory of processes, generalised random fields, estimation theory and information geometry, are reviewed. Their quantum versions are then described.

Classical Probability and Quantum Outcomes

There is a contact problem between classical probability and quantum outcomes. Thus, a standard result from classical probability on the existence of joint distributions ultimately implies that all quantum observables must commute. An essential task here is a closer identification of this conflict based on deriving commutativity from the weakest possible assumptions, and showing that stronger a...

Geometrical structures of photographic and stereoscopic spaces.

Two experiments were conducted to investigate the geometrical structures of photographic and stereoscopic spaces. In Experiment 1, it was investigated how accurately photographic space reproduces real physical space, and the geometrical structure of photographic space was compared with that of visual space. As a result, the mapping function of distance between photographic and physical spaces (...

Quantum Probability Spaces