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dc.contributor.authorVourdas, Apostolos
dc.date.accessioned2022-12-02T09:53:23Z
dc.date.accessioned2022-12-07T15:41:42Z
dc.date.available2022-12-02T09:53:23Z
dc.date.available2022-12-07T15:41:42Z
dc.date.issued2022-11
dc.identifier.citationVourdas A (2022) Grothendieck bound in a single quantum system. Journal of Physics A: Mathematical and Theoretical. 55: 435206.en_US
dc.identifier.urihttp://hdl.handle.net/10454/19241
dc.descriptionYesen_US
dc.description.abstractGrothendieck's bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the violation of Bell-like inequalities. Roughly speaking the Grothendieck theorem considers a 'classical' quadratic form ${\cal C}$ that uses complex numbers in the unit disc, and takes values less than 1. It then proves that if the complex numbers are replaced with vectors in the unit ball of the Hilbert space, then the 'quantum' quadratic form ${\cal Q}$ might take values greater than 1, up to the complex Grothendieck constant $k_\mathrm G$. The Grothendieck theorem is reformulated here in terms of arbitrary matrices (which are multiplied with appropriate normalisation prefactors), so that it is directly applicable to quantum quantities. The emphasis in the paper is in the 'Grothendieck region' $(1,k_\mathrm G)$, which is a classically forbidden region in the sense that ${\cal C}$ cannot take values in it. Necessary (but not sufficient) conditions for ${\cal Q}$ taking values in the Grothendieck region are given. Two examples that involve physical quantities in systems with six and 12-dimensional Hilbert space, are shown to lead to ${\cal Q}$ in the Grothendieck region $(1,k_\mathrm G)$. They involve projectors of the overlaps of novel generalised coherent states that resolve the identity and have a discrete isotropy.en_US
dc.language.isoenen_US
dc.rights© 2022 IOP Publishing. This is an author-created, un-copyedited version of an article accepted for publication/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/ac9dcf.en_US
dc.subjectGrothendiecken_US
dc.subjectSingle quantum systemen_US
dc.titleGrothendieck bound in a single quantum systemen_US
dc.status.refereedYesen_US
dc.date.Accepted2022-10-26
dc.date.application2022-11-07
dc.typeArticleen_US
dc.type.versionAccepted manuscripten_US
dc.identifier.doihttps://doi.org/10.1088/1751-8121/ac9dcf
dc.rights.licenseUnspecifieden_US
dc.date.updated2022-12-02T09:53:26Z
refterms.dateFOA2022-12-07T15:42:10Z
dc.openaccess.statusopenAccessen_US


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