Independence and totalness of subspaces in phase space methods

Journal Article · Sun Apr 15 04:00:00 EDT 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.02.010· OSTI ID:22848316

The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota’s formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.

• OSTI ID: 22848316
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 391; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTRIBUTION
DUALITY
HILBERT SPACE
OPERATION
PHASE SPACE
PROBABILITY
QUANTUM SYSTEMS