标题： 从消失的保性性中吸引子 显示英文标题

标题： STU attractors from vanishing concurrence

摘要： 纠缠态是一个表征纯态内部两部分量子关联的纠缠测度，在一个$n$-量子比特系统的{\it 混合}态中。我们证明了在将 STU 模型中的荷与模量以及$N=2$，$d=4$超引力组织为一个三量子比特态之后，对于静态极端球对称 BPS 黑洞解，在视界上所有两部分纠缠度量消失的条件等价于吸引子方程。由此得出，由三重纠缠测度给出的黑洞宏观熵可以重新解释为表征任意两部分分裂的{\it 纯的}态纠缠的线性熵。对于 BPS 和非 BPS 情况都得到了纠缠度量的具体表达式，并且它们在视界上的消失也得到了证明。 显示英文摘要

摘要： Concurrence is an entanglement measure characterizing the {\it mixed} state bipartite correlations inside of a pure state of an $n$-qubit system. We show that after organizing the charges and the moduli in the STU model of $N=2$, $d=4$ supergravity to a three-qubit state, for static extremal spherically symmetric BPS black hole solutions the vanishing condition for all of the bipartite concurrences on the horizon is equivalent to the attractor equations. As a result of this the macroscopic black hole entropy given by the three-tangle can be reinterpreted as a linear entropy characterizing the {\it pure} state entanglement for an arbitrary bipartite split. Both for the BPS and non-BPS cases explicit expressions for the concurrences are obtained, with their vanishing on the horizon is demonstrated.