Partial islands and subregion complexity in geometric secret-sharing model

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 AdS3. 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.

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Geometric secret sharing in a model of Hawking radiation

Journal of High Energy Physics ◽

10.1007/jhep01(2021)177 ◽

2021 ◽

Vol 2021 (1) ◽

Cited By ~ 3

Author(s):

Vijay Balasubramanian ◽

Arjun Kar ◽

Onkar Parrikar ◽

Gábor Sárosi ◽

Tomonori Ugajin

Keyword(s):

Field Theory ◽

Black Hole ◽

Secret Sharing ◽

Hawking Radiation ◽

Entanglement Entropy ◽

Three Dimensional ◽

External Radiation ◽

Sharing Scheme ◽

Black Hole Interior ◽

Pass Through

Abstract We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This “inception black hole” can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed “island formula”. We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

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