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dc.contributor.authorVourdas, Apostolos*
dc.date.accessioned2018-03-19T14:37:46Z
dc.date.available2018-03-19T14:37:46Z
dc.date.issued2018-04
dc.identifier.citationVourdas A (2018) Independence and totalness of subspaces in phase space methods. Annals of Physics. 391: 83-111.en_US
dc.identifier.urihttp://hdl.handle.net/10454/15241
dc.descriptionYesen_US
dc.description.abstractThe 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.en_US
dc.language.isoenen_US
dc.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.en_US
dc.subjectPhase space methods; Independence; Non-distributivityen_US
dc.titleIndependence and totalness of subspaces in phase space methodsen_US
dc.status.refereedYesen_US
dc.date.application2018-02-19
dc.typeArticleen_US
dc.type.versionAccepted Manuscripten_US
dc.identifier.doihttps://doi.org/10.1016/j.aop.2018.02.010
refterms.dateFOA2019-02-20T09:47:57Z
dc.date.accepted2018-02-14


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