Tensor Network Models of Unitary Black Hole Evaporation

TL;DR

This paper introduces tensor network toy models to analyze quantum information properties of black hole radiation, providing new entanglement measures and universal results for certain model classes.

Contribution

It develops a framework using isometries and tensor networks to study black hole radiation entanglement, including generalized entropy measures and universality results.

Findings

Entanglement structure is universal when radiation Hilbert space dimension matches initial microstates.

Models with tripartite tensors with maximally mixed subsystems best capture black hole horizon properties.

Derived formulas for average entanglement measures over initial black hole states.

Abstract

We introduce a general class of toy models to study the quantum information-theoretic properties of black hole radiation. The models are governed by a set of isometries that specify how microstates of the black hole at a given energy evolve to entangled states of a tensor product black-hole/radiation Hilbert space. The final state of the black hole radiation is conveniently summarized by a tensor network built from these isometries. We introduce a set of quantities generalizing the Renyi entropies that provide a complete set of bipartite/multipartite entanglement measures, and give a general formula for the average of these over initial black hole states in terms of the isometries defining the model. For models where the dimension of the final tensor product radiation Hilbert space is the same as that of the space of initial black hole microstates, the entanglement structure is universal, independent of the choice of isometries. In the more general case, we find that models which best capture the "information-free" property of black hole horizons are those whose isometries are tensors corresponding to states of tripartite systems with maximally mixed subsystems.