论文标题
四个胜任状态的分类
Classification of four-rebit states
论文作者
论文摘要
我们对四个队的状态进行了分类，也就是说，我们将$ \ wideHat {g}（\ mathbb r）= \ mathrm {\ mathop {sl}}（2，\ mathbb r）^4 $在太空中的$（\ Mathbb r^2）^2）^{\ otimes 4} $中进行分类。这是量子信息理论中众所周知的SLOCC操作的真正类似物。通过构建$ \ wideHat {g}（\ mathbb r）$ - 模块$（\ mathbb r^2）^{\ otimes 4} $通过$ \ mathbb z/2 \ mathbb z/2 \ mathbb z $ - 简单的splite lie lie lie elgebra of Type $ d_4 $的简单分裂元素的级别，ORBITS; Nilpotent Orbits已分类为Dietrich等人。 （2017年），在理论物理学中产生应用（$ \ Mathcal {n} = 2的stu模型中的极端黑洞，d = 4 $ supergravity，请参见Ruggeri和Trigiante（2017））。在这里，我们关注的是半岛和混合轨道，我们将这些轨道与基于Galois的同一个同种学的最近开发的方法进行了分类，请参见Borovoi等。 （2021）。这些轨道与Stu模型中非超级（或极端过度旋转）和两个中心极端黑洞溶液的分类有关。
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.
