dc.contributor.author Vourdas, Apostolos dc.date.accessioned 2022-12-02T09:53:23Z dc.date.accessioned 2022-12-07T15:41:42Z dc.date.available 2022-12-02T09:53:23Z dc.date.available 2022-12-07T15:41:42Z dc.date.issued 2022-11 dc.identifier.citation Vourdas A (2022) Grothendieck bound in a single quantum system. Journal of Physics A: Mathematical and Theoretical. 55: 435206. en_US dc.identifier.uri http://hdl.handle.net/10454/19241 dc.description Yes en_US dc.description.abstract Grothendieck'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.iso en en_US dc.relation.isreferencedby https://doi.org/10.1088/1751-8121/ac9dcf en_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.subject Grothendieck en_US dc.subject Single quantum system en_US dc.title Grothendieck bound in a single quantum system en_US dc.status.refereed Yes en_US dc.date.Accepted 2022-10-26 dc.date.application 2022-11-07 dc.type Article en_US dc.date.EndofEmbargo 2023-11-07 dc.type.version Accepted manuscript en_US dc.description.publicnotes The full-text of this article will be released for public view at the end of the publisher embargo on 07 Nov 2023. en_US dc.rights.license Unspecified en_US dc.date.updated 2022-12-02T09:53:26Z refterms.dateFOA 2022-12-07T15:42:10Z dc.openaccess.status embargoedAccess en_US
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