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

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.

53 pages, 24 figures; accepted Class. and Quant. Grav (2Feb2015)

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Cited by in corpus (9)

• Introduction to the Absolute Brightness and Number Statistics in Spontaneous Parametric Down-Conversion
• One-shot decoupling and Page curves from a dynamical model for black hole evaporation
• Quantum Circuit Model for a Uniformly Accelerated Mirror
• Entanglement of self interacting scalar fields in an expanding spacetime
• Phase effects in coherently-stimulated down-conversion with a quantized pump field
• Unconditional remote entanglement using second-harmonic generation and twin two-mode squeezed vacuum states
• Stimulated Emission of Radiation and the Black Hole Information Problem
• Paradox No More: How Stimulated Emission of Radiation Preserves Information Absorbed by Black Holes
• Spontaneous parametric down conversion with a depleted pump as an analogue for black hole evaporation/particle production