标题： 受激辐射与黑洞信息问题 显示英文标题

标题： Stimulated Emission of Radiation and the Black Hole Information Problem

摘要： 黑洞的量子理论为研究广义相对论和量子场论的交集打开了一扇窗口，但关于经典信息在黑洞视界处的命运以及蒸发过程的幺正性方面的感知悖论，使得研究人员开始质疑物理学的基本原理。 在这篇教学性综述中，我澄清了这样一个事实的影响：黑洞不仅会自发地发射辐射，还会通过受激方式发射近似克隆的那些场，以响应下落的物质和辐射。 我回顾了基于爱因斯坦对黑体处理的早期纯统计论证，然后证明黑洞的霍尔沃容量（通过量子信道传输经典信息的能力）始终是正的。 接着，我展示了受激发射如何使黑洞变成几乎最优的量子克隆机，并进一步讨论黑洞传输量子信息的能力。 利用黑洞物理与非线性光学之间的类比，我展示了使用黑洞$S$-矩阵路径积分的离散化来计算黑洞随时间演化的结果，得到了行为良好的页面曲线，表明黑洞蒸发是幺正的。 最后，我推测黑洞辐射受激发射可能带来的可观测后果。 显示英文摘要

摘要： The quantum theory of black holes has opened up a window to study the intersection of general relativity and quantum field theory, but perceived paradoxes concerning the fate of classical information directed at a black hole horizon, as well as concerning the unitarity of the evaporation process, have led researchers to question the very foundations of physics. In this pedagogical review I clarify the ramifications of the fact that black holes not only emit radiation spontaneously, but also respond to infalling matter and radiation by emitting approximate clones of those fields in a stimulated manner. I review early purely statistical arguments based on Einstein's treatment of black bodies, and then show that the Holevo capacity of the black hole (the capacity to transmit classical information through a quantum channel) is always positive. I then show how stimulated emission turns the black hole into an almost optimal quantum cloning machine, and furthermore discuss the capacity of black holes to transmit quantum information. Taking advantage of an analogy between black hole physics and non-linear optics I show that a calculation of the evolution of a black hole over time, using a discretization of the black hole $S$-matrix path integral, yields well-behaved Page curves suggesting that black hole evaporation is unitary. Finally, I speculate about possible observable consequences of stimulated emission of radiation in black holes.