论文标题
反射的熵用于蒸发黑洞
Reflected Entropy for an Evaporating Black Hole
论文作者
论文摘要
我们将反射的熵作为黑洞蒸发中的相关度量。作为双分裂混合状态的度量，可以在黑洞和辐射，辐射和辐射之间计算反射的熵。我们在三个不同的模型中计算反射的熵曲线：三个虫孔模型，三个维度的世界末日（EOW）Brane模型和二维永恒的黑洞加上CFT模型。对于三侧虫洞模型，我们发现反射的熵对岛横截面是双重的。辐射和黑洞之间的反射熵在早期增加，然后减少到零，类似于页面曲线，但随后过渡时间。辐射和辐射之间的反射熵首先增加，然后饱和。对于EOW Brane模型，发现反射熵的类似行为。 我们提出了一个量子极端表面，用于反射熵，我们称之为量子极端横截面。在永恒的黑洞加上CFT模型中，我们通过将右半视为左侧的规范纯化，找到了一个通用的熵熵公式，该公式是其区域项。有趣的是，左黑洞和左辐射之间的反射熵曲线只不过是页面曲线。我们还发现，左黑洞和右黑洞之间的反射熵降低，并在较晚的时间降至零。辐射和辐射之间的反射熵在较早的时间增加，并在晚期饱和。
We study reflected entropy as a correlation measure in black hole evaporation. As a measure for bipartite mixed states, reflected entropy can be computed between black hole and radiation, radiation and radiation. We compute reflected entropy curves in three different models: 3-side wormhole model, End-of-the-World (EOW) brane model in three dimensions and two-dimensional eternal black hole plus CFT model. For 3-side wormhole model, we find that reflected entropy is dual to island cross sections. The reflected entropy between radiation and black hole increases at early time and then decreases to zero, similar to Page curve, but with a later transition time. The reflected entropy between radiation and radiation first increases and then saturates. For the EOW brane model, similar behaviors of reflected entropy are found. We propose a quantum extremal surface for reflected entropy, which we call quantum extremal cross section. In the eternal black hole plus CFT model, we find a generalized formula for reflected entropy with island cross section as its area term by considering the right half as the canonical purification of the left. Interestingly, the reflected entropy curve between the left black hole and the left radiation is nothing but the Page curve. We also find that reflected entropy between the left black hole and the right black hole decreases and goes to zero at late time. The reflected entropy between radiation and radiation increases at early time and saturates at late time.
