We classify states of four rebits, that is, we classify the orbits of the group (G) over cap (R) = SL(2, R)(4) in the space (R-2)(circle times 4). This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the (G) over cap (R)-module (R-2)(circle times 4) via a Z/2Z-grading of the simple split real Lie algebra of type D-4, the orbits are divided into three groups: semisimple, nilpotent and mixed. The nilpotent orbits have been classified in Dietrich et al. (2017) [26], yielding applications in theoretical physics (extremal black holes in the STU model of N = 2, D = 4 supergravity, see Ruggeri and Trigiante (2017) [51]). Here we focus on the semisimple and mixed orbits which we classify with recently developed methods based on Galois cohomology, see Borovoi et al. (2021) [8,9]. These orbits are relevant to the classification of non-extremal (or extremal over-rotating) and two-center extremal black hole solutions in the STU model. (c) 2022 Elsevier B.V. All rights reserved.

Classification of four-rebit states / Dietrich, H.; de Graaf, W. A.; Marrani, A.; Origlia, M.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 179:(2022), pp. 10461001-10461031. [10.1016/j.geomphys.2022.104610]

Classification of four-rebit states

Dietrich H.;de Graaf W. A.;Marrani A.;
2022-01-01

Abstract

We classify states of four rebits, that is, we classify the orbits of the group (G) over cap (R) = SL(2, R)(4) in the space (R-2)(circle times 4). This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the (G) over cap (R)-module (R-2)(circle times 4) via a Z/2Z-grading of the simple split real Lie algebra of type D-4, the orbits are divided into three groups: semisimple, nilpotent and mixed. The nilpotent orbits have been classified in Dietrich et al. (2017) [26], yielding applications in theoretical physics (extremal black holes in the STU model of N = 2, D = 4 supergravity, see Ruggeri and Trigiante (2017) [51]). Here we focus on the semisimple and mixed orbits which we classify with recently developed methods based on Galois cohomology, see Borovoi et al. (2021) [8,9]. These orbits are relevant to the classification of non-extremal (or extremal over-rotating) and two-center extremal black hole solutions in the STU model. (c) 2022 Elsevier B.V. All rights reserved.
2022
Dietrich, H.; de Graaf, W. A.; Marrani, A.; Origlia, M.
Classification of four-rebit states / Dietrich, H.; de Graaf, W. A.; Marrani, A.; Origlia, M.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 179:(2022), pp. 10461001-10461031. [10.1016/j.geomphys.2022.104610]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/373691
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