Parametric down conversion with a depleted pump as a model for classical information transmission capacity of quantum black holes

TL;DR

This paper models black hole particle emission as a quantum optical process akin to parametric down conversion, analyzing information transmission capacity and entanglement dynamics during black hole evaporation.

Contribution

It introduces a dynamical pump mode representing black hole energy, coupling emitted radiation modes, and explores unitarity, entanglement, and information flow in black hole evaporation.

Findings

Verified the Page time for information release in the model

Analyzed entanglement dynamics between emitted particles

Explored effects of black hole evaporation on external entangled modes

Abstract

In this paper we extend the investigation of Adami and Ver Steeg [Class. Quantum Grav. \textbf{31}, 075015 (2014)] to treat the process of black hole particle emission effectively as the analogous quantum optical process of parametric down conversion (PDC) with a dynamical (depleted vs. non-depleted) `pump' source mode which models the evaporating black hole (BH) energy degree of freedom. We investigate both the short time (non-depleted pump) and long time (depleted pump) regimes of the quantum state and its impact on the Holevo channel capacity for communicating information from the far past to the far future in the presence of Hawking radiation. The new feature introduced in this work is the coupling of the emitted Hawking radiation modes through the common black hole `source pump' mode which phenomenologically represents a quantized energy degree of freedom of the gravitational field. This (zero-dimensional) model serves as a simplified arena to explore BH particle production/evaporation and back-action effects under an explicitly unitary evolution which enforces quantized energy/particle conservation. Within our analogous quantum optical model we examine the entanglement between two emitted particle/anti-particle and anti-particle/particle pairs coupled via the black hole (BH) evaporating `pump' source. We also analytically and dynamically verify the `Page information time' for our model which refers to the conventionally held belief that the information in the BH radiation becomes significant after the black hole has evaporated half its initial energy into the outgoing radiation. Lastly, we investigate the effect of BH particle production/evaporation on two modes in the exterior region of the BH event horizon that are initially maximally entangled, when one mode falls inward and interacts with the black hole, and the other remains forever outside and non-interacting.