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Publication Date
2018-04
End of Embargo
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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.
Peer-Reviewed
Yes
Open Access status
Accepted for publication
2018-02-14
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Awarded
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Additional title
Abstract
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.
Version
Accepted Manuscript
Citation
Vourdas A (2018) Independence and totalness of subspaces in phase space methods.
Annals of Physics. 391: 83-111.
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Type
Article