Holevo Information and Ensemble Theory of Gravity

TL;DR

This paper explores the role of Holevo information in quantum gravity, proposing a conjecture on its holographic bulk formula and validating it through calculations in tensor networks and the SYK model.

Contribution

It introduces a conjecture linking Holevo information to holographic gravity and tests it using random tensor networks and SYK model states.

Findings

Holevo information bounds accessible classical data in quantum ensembles.

Conjecture on holographic bulk formula for Holevo information proposed.

Results in SYK model support the conjecture.

Abstract

Holevo information is an upper bound for the accessible classical information of an ensemble of quantum states. In this work, we use Holevo information to investigate the ensemble theory interpretation of quantum gravity. We study the Holevo information in random tensor network states, where the random parameters are the random tensors at each vertex. Based on the results in random tensor network models, we propose a conjecture on the holographic bulk formula of the Holevo information in the gravity case. As concrete examples of holographic systems, we compute the Holevo information in the ensemble of thermal states and thermo-field double states in the Sachdev-Ye-Kitaev model. The results are consistent with our conjecture.