Yes / 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.
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/15241 |
| Date | 19 February 2018 |
| Creators | Vourdas, Apostolos |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Article, Accepted Manuscript |
| Rights | © 2018 Elsevier. Reproduced in accordance with the publisher's selfarchiving policy. This manuscript version is made available under the CC-BY-NC-ND 4.0 license. |
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