Entangled Harmonic Oscillators and Space-Time Entanglement

dc.contributor.authorBaşkal, Sibel
dc.contributor.authorKim, Young S.
dc.contributor.authorNoz, Marilyn E.
dc.date.accessioned2023-12-05T15:46:35Z
dc.date.available2023-12-05T15:46:35Z
dc.date.issued2016-06-28
dc.description.abstractThe mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of the 𝑂(3,2) de Sitter group containing two 𝑂(3,1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of the 𝑆𝑝(4) group, which serves as the basic language for two-mode squeezed states. Since the 𝑆𝑝(4) symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified.
dc.description.urihttps://doi.org/10.3390/sym8070055
dc.identifierhttps://doi.org/10.13016/dspace/lzck-rxrw
dc.identifier.citationBaşkal, S.; Kim, Y.S.; Noz, M.E. Entangled Harmonic Oscillators and Space-Time Entanglement. Symmetry 2016, 8, 55.
dc.identifier.urihttp://hdl.handle.net/1903/31536
dc.language.isoen_US
dc.publisherMDPI
dc.relation.isAvailableAtCollege of Computer, Mathematical & Natural Sciencesen_us
dc.relation.isAvailableAtPhysicsen_us
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_us
dc.relation.isAvailableAtUniversity of Maryland (College Park, MD)en_us
dc.subjectGaussian entanglement
dc.subjecttwo coupled harmonic oscillators
dc.subjectcoupled Lorentz groups
dc.subjectspace-time separation
dc.subjectWigner's little groups
dc.subjectO(3, 2) group
dc.subjectDirac's generators for two coupled oscillators
dc.titleEntangled Harmonic Oscillators and Space-Time Entanglement
dc.typeArticle
local.equitableAccessSubmissionNo

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