Stimulated Emission of Radiation and the Black Hole Information Problem

TL;DR

This paper explores how stimulated emission in black holes affects information transfer and unitarity, suggesting black hole evaporation may be consistent with quantum theory and proposing observable consequences.

Contribution

It demonstrates that stimulated emission makes black holes effective quantum cloning machines and supports the unitarity of black hole evaporation through a novel analogy with non-linear optics.

Findings

Black holes can transmit classical information via stimulated emission.

Stimulated emission turns black holes into near-optimal quantum cloning machines.

Page curves indicate black hole evaporation is unitary.

Abstract

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.