A concept of measuring the quantum distance between two different quantum states that is called quantum information metric has been presented. The holographic principle (anti–de Sitter/conformal field theory) suggests that the quantum information metric G λ λ between perturbed state and unperturbed state in field theory has a dual description in the classical gravity. In this work we calculate the quantum information metric of a theory that is dual to a conical defect geometry and we show that it is n times the one of its covering space. We also give a holographic check for our result in the gravity side. Meanwhile, it was argued that G λ λ is dual to a codimension-one surface in spacetime and satisfies G λ λ = n d · Vol ( Σ max ) / L d . We show that the coefficient n d for conical defect should be rescaled by n 2 from the one for anti–de Sitter space. A limit case of conical defect—the massless Banados-Teitelboim-Zannelli (BTZ) black hole—is also considered. We show that the quantum information metric of a massless BTZ black hole disagrees with the one obtained by taking the vanishing temperature limit in BTZ black hole. This provides a new arena in differentiating the different phases between BTZ spacetime and its massless cousin.
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机译：提出了一种测量两个不同量子态之间的量子距离的概念，称为量子信息度量。全息原理（反Sitter /共形场理论）表明，场论中扰动态和非扰动态之间的量子信息度量Gλλ在经典引力中具有双重描述。在这项工作中，我们计算了一种理论的量子信息度量，该度量是圆锥形缺陷几何的对偶，并且我们证明它是其覆盖空间之一的n倍。我们还将在重力方面对结果进行全息检查。同时，有人认为，Gλλ是时空对一个余维一表面的对偶，并且满足Gλλ= n d·Vol（Σmax）/ L d。我们表明，圆锥形缺陷的系数n d应该从anti-de Sitter空间的一个系数重新定标n 2。还考虑了圆锥形缺陷的极限情况-无质量的Banados-Teitelboim-Zannelli（BTZ）黑洞。我们表明，无质量BTZ黑洞的量子信息度量与通过采取BTZ黑洞中消失的温度极限获得的量子信息度量不一致。这为区分BTZ时空与其无质量表亲之间的不同阶段提供了新的舞台。
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