Holevo Information and Ensemble Theory of Gravity

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.

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Cited by in corpus (9)

• Fun with replicas: tripartitions in tensor networks and gravity
• Random tensor networks with nontrivial links
• The Entanglement Wedge of Unknown Couplings
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• A comment on a fine-grained description of evaporating black holes with baby universes
• Quantum Error Correction in SYK and Bulk Emergence
• Collisions of localized shocks and quantum circuits
• Phase-transition-like behavior in information retrieval of a quantum scrambled random circuit system
• Baby universes, ensemble averages and factorizations with matters