Partial islands and subregion complexity in geometric secret-sharing model

TL;DR

This paper analyzes the holographic complexity of radiation in a geometric secret-sharing model, revealing how partial access to islands affects complexity evolution and introduces a new perspective on information recovery.

Contribution

It introduces a model using multiboundary wormholes to study subregion complexity and reveals how partial island access impacts complexity and information recovery.

Findings

Complexity exhibits a jump at secret-sharing time beyond Page time.

Minimal surfaces access only part of the island, not the entire region.

Partial access to islands relates to classical Markov recovery.

Abstract

We compute the holographic subregion complexity of a radiation subsystem in a geometric secret-sharing model of Hawking radiation in the "complexity = volume" proposal. The model is constructed using multiboundary wormhole geometries in AdS$_{3}$. The entanglement curve for secret-sharing captures a crossover between two minimal curves in the geometry apart from the usual eternal Page curve present for the complete radiation entanglement. We compute the complexity dual to the secret-sharing minimal surfaces and study their "time" evolution. When we have access to a small part of the radiation, the complexity shows a jump at the secret-sharing time larger than the Page time. Moreover, the minimal surfaces do not have access to the entire island region for this particular case. They can only access it partially. We describe this inaccessibility in the context of "classical" Markov recovery.