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dc.contributor.authorVourdas, Apostolos
dc.date.accessioned2020-05-20T15:08:09Z
dc.date.available2020-05-20T15:08:09Z
dc.date.issued2020-05
dc.identifier.citationVourdas A (2020) Equivalence classes of coherent projectors in a Hilbert space with prime dimension: Q functions and their Gini index. Journal of Physics A: Mathematical and Theoretical. 53(21): 215201.en_US
dc.identifier.urihttp://hdl.handle.net/10454/17828
dc.descriptionYesen_US
dc.description.abstractCoherent subspaces spanned by a finite number of coherent states are introduced, in a quantum system with Hilbert space that has odd prime dimension d. The set of all coherent subspaces is partitioned into equivalence classes, with d 2 subspaces in each class. The corresponding coherent projectors within an equivalence class, have the 'closure under displacements property' and also resolve the identity. Different equivalence classes provide different granularisation of the Hilbert space, and they form a partial order 'coarser' (and 'finer'). In the case of a two-dimensional coherent subspace spanned by two coherent states, the corresponding projector (of rank 2) is different than the sum of the two projectors to the subspaces related to each of the two coherent states. We quantify this with 'non-addditivity operators' which are a measure of quantum interference in phase space, and also of the non-commutativity of the projectors. Generalized Q and P functions of density matrices, which are based on coherent projectors in a given equivalence class, are introduced. Analogues of the Lorenz values and the Gini index (which are popular quantities in mathematical economics) are used here to quantify the inequality in the distribution of the Q function of a quantum state, within the granular structure of the Hilbert space. A comparison is made between Lorenz values and the Gini index for the cases of coarse and also fine granularisation of the Hilbert space. Lorenz values require an ordering of the d 2 values of the Q function of a density matrix, and this leads to the ranking permutation of a density matrix, and to comonotonic density matrices (which have the same ranking permutation). The Lorenz values are a superadditive function and the Gini index is a subadditive function (they are both additive quantities for comonotonic density matrices). Various examples demonstrate these ideas.en_US
dc.language.isoenen_US
dc.relation.isreferencedbyhttps://doi.org/10.1088/1751-8121/ab86e0en_US
dc.rightsThis is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/ab86e0.en_US
dc.subjectCoherent projectorsen_US
dc.subjectGini indexen_US
dc.subjectPhase space methodsen_US
dc.titleEquivalence classes of coherent projectors in a Hilbert space with prime dimension: Q functions and their Gini indexen_US
dc.status.refereedYesen_US
dc.date.Accepted2020-04-06
dc.date.application2020-04-06
dc.typeArticleen_US
dc.date.EndofEmbargo2021-04-07
dc.type.versionAccepted manuscripten_US
dc.description.publicnotesThe full-text of this article will be released for public view at the end of the publisher embargo on 07 Apr 2021.en_US
refterms.dateFOA2020-05-20T15:09:23Z


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