Title: Quantum Relative Entropy implies the Semiclassical Einstein Equations Show Chinese title

Title: 量子相对熵蕴含半经典爱因斯坦方程

Abstract: We prove that the semiclassical Einstein equations emerge directly from quantum information theory. Using modular theory, we establish that the relative entropy between the vacuum state and coherent excitations of a scalar quantum field on a bifurcate Killing horizon is given by the energy flux across the horizon. Under the assumption of the Bekenstein-Hawking entropy-area formula, this energy flux is proportional to a variation in the surface area of the horizon cross section. The semiclassical Einstein equations follow automatically from this identification. Our approach provides a rigorous quantum field theoretic generalization of Jacobson's thermodynamic derivation of Einstein's equations, replacing classical thermodynamic entropy with the well-defined quantum relative (Araki-Uhlmann) entropy. This suggests that quantum information plays a fundamental role in what is seen as a zeroth order approximation of a theory of quantum gravity, namely quantum field theory in curved spacetimes. Show Chinese abstract

Abstract: 我们证明半经典爱因斯坦方程直接来自量子信息理论。 利用模论，我们确立了在分叉的Killing视界上标量量子场的真空态与相干激发之间的相对熵由视界上的能量通量给出。 在假设贝肯斯坦-霍金熵-面积公式的前提下，这个能量通量与视界截面的表面积的变化成比例。 从这种识别中，半经典爱因斯坦方程自动得出。 我们的方法提供了一种严格的量子场论推广，用于雅各布森对爱因斯坦方程的热力学推导，用明确的量子相对（阿拉基-乌尔曼）熵取代了经典的热力学熵。 这表明量子信息在被视为量子引力理论的零阶近似，即弯曲时空中的量子场论中起着基本作用。