Classification of four-rebit states

• URL: http://arxiv.org/abs/2201.11777v2
• Date: Tue, 1 Feb 2022 12:59:29 GMT
• Title: Classification of four-rebit states
• Authors: Heiko Dietrich, Willem A. de Graaf, Alessio Marrani, Marcos Origlia
• Abstract summary: We classify states of four rebits, that is, we classify the orbits of the group $widehatG(mathbb R) = mathrmmathopSL (2,mathbb R)4$ in the space(mathbb R2)otimes 4$. This is the real analogon of the well-known SLOCC operations in quantum information theory.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We classify states of four rebits, that is, we classify the orbits of the group $\widehat{G}(\mathbb R) = \mathrm{\mathop{SL}}(2,\mathbb R)^4$ in the space $(\mathbb R^2)^{\otimes 4}$. This is the real analogon of the well-known SLOCC operations in quantum information theory. By constructing the $\widehat{G}(\mathbb R)$-module $(\mathbb R^2)^{\otimes 4}$ via a $\mathbb Z/2\mathbb Z$-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), yielding applications in theoretical physics (extremal black holes in the STU model of $\mathcal{N}=2, D=4$ supergravity, see Ruggeri and Trigiante (2017)). 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). 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.

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