Islands and mixed states in closed universes

Seamus Fallows; Simon F. Ross

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Islands and mixed states in closed universes

Seamus Fallows, Simon F. Ross

High Energy Physics - Theory · Submitted 26 Mar 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.

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What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.42 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.89 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system. We use braneworlds in three-dimensional multiboundary wormhole geometries as a model to explore what happens when the non-gravitating system has several components. The braneworld can be either completely contained in the entanglement wedge of one of the non-gravitating systems or split between them. In the former case, entanglement with the other system leads to a mixed state in the closed universe, unlike in simpler setups with a single quantum system, where the closed universe was necessarily in a pure state. We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system.	contribution 0.96	0.84	0.05	asserted 0.59
s1	We use braneworlds in three-dimensional multiboundary wormhole geometries as a model to explore what happens when the non-gravitating system has several components.	method 0.99	0.81	0.04	asserted 0.97
s2	The braneworld can be either completely contained in the entanglement wedge of one of the non-gravitating systems or split between them.	method 0.63	0.43	0.08	asserted 0.70
s3	In the former case, entanglement with the other system leads to a mixed state in the closed universe, unlike in simpler setups with a single quantum system, where the closed universe was necessarily in a pure state.	result 0.96	0.75	0.48	asserted 1.00
s4	We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.	result 1.00	0.94	0.43	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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arXiv listing abstract v3

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The paper

Original abstract

We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system. We use braneworlds in three-dimensional multiboundary wormhole geometries as a model to explore what happens when the non-gravitating system has several components. The braneworld can be either completely contained in the entanglement wedge of one of the non-gravitating systems or split between them. In the former case, entanglement with the other system leads to a mixed state in the closed universe, unlike in simpler setups with a single quantum system, where the closed universe was necessarily in a pure state. We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.

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References

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Cosmology from the vacuum
hep-th 2022-03 conditional novelty 6.0 of 10

Cosmological observables in a recollapsing negative-Lambda universe are argued to equal, by analytic continuation, vacuum observables in a dual static AdS wormhole, so perturbations can be computed without inflation.
Entanglement between two gravitating universes
hep-th 2021-04 conditional novelty 6.0 of 10

When two gravitating universes are highly entangled, the gravitational path integral is dominated by a wormhole that glues them into one connected spacetime, and the resulting entropy formula keeps the state unitary.
Entropy of Hawking Radiation for Two-Sided Hyperscaling Violating Black Branes
hep-th 2021-12 conditional novelty 5.0 of 10

For a hyperscaling-violating black brane with hyperscaling-violating matter, the Hawking-radiation entropy grows exponentially before the Page time and the Page time scales as log(1/G_N).
Defect Extremal Surface for Reflected Entropy
hep-th 2021-08 conditional novelty 5.0 of 10

A defect extremal surface formula for reflected entropy reproduces the boundary island formula in AdS3/BCFT2 and yields Page-curve behavior in an evaporating black hole model.
Page Curve from Defect Extremal Surface and Island in Higher Dimensions
hep-th 2021-05 conditional novelty 5.0 of 10

In 2+1 dimensions the defect extremal surface and island formula give identical Page curves, but in higher dimensions the defect extremal surface gives systematically smaller entropy, which the authors read as a UV co...

Show 1 more citing papers

Replica wormholes and capacity of entanglement
hep-th 2021-05 conditional novelty 5.0 of 10

A replica path integral formula for the capacity of entanglement in JT gravity is derived and checked against the thermal heat capacity in a high temperature eternal black hole.

How the literature uses it

20 arXiv papers cite this in 23 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 11 sentences without a confident label

Uses its method or tool 1 paper

From the Polyakov action <ref>, the transverse area term of a co-dimension two surface $χ$ appearing in the island formula may be obtained as follows [ref] [equation] where in the last equality, we have used the Brown-Henneaux relations as well as the fact that the Ricci scalar on the brane $Σ$ is given by [ref] [equation]

Holographic Reflected Entropy and Islands in Interface CFTs · Reflected entropy from island prescription: vacuum state · 0.82

Cites it as background 10 papers

The development relies on the quantum extremal surface formula for the fine grained entropy, which was inspired from the quantum corrected Ryu-Takayanagi formula in computing holographic entanglement entropy [ref] .

Defect Extremal Surface for Reflected Entropy · Introduction · 0.94
For recent related works, see [ref] .

Page Curve from Defect Extremal Surface and Island in Higher Dimensions · Introduction · 0.99
Islands have also been studied when a gravitating system and another system are entangled but not coupled [ref] .

Inconsistency of Islands in Theories with Long-Range Gravity · Islands in decoupled systems · 1.00

What it cites · 46 sentences without a confident label

Builds on 7 papers

We will build this model by adding an end of the world brane to the multiboundary wormhole solutions discussed in [ref] .

Holography and wormholes in 2+1 dimensions · Review of multiboundary wormholes · 0.88
We will build this model by adding an end of the world brane to the multiboundary wormhole solutions discussed in [ref] .

Multiboundary Wormholes and Holographic Entanglement · Review of multiboundary wormholes · 0.88
We will build this model by adding an end of the world brane to the multiboundary wormhole solutions discussed in [ref] .

Hot multiboundary wormholes from bipartite entanglement · Review of multiboundary wormholes · 0.88

Uses the method or tool of 2 papers

We will describe the quotient using the $SL(2,ℝ)$ representation of AdS$_3$, following [ref] .[For another perspective on the construction of the three-boundary wormhole see [ref] .] A point in the spacetime is described by an $SL(2,ℝ)$ matrix $p$, and the spacetime metric is $ds^2 = - (dp)$.

Entanglement entropy in three dimensional gravity · Review of multiboundary wormholes · 0.93
We will describe the quotient using the $SL(2,ℝ)$ representation of AdS$_3$, following [ref] .[For another perspective on the construction of the three-boundary wormhole see [ref] .] A point in the spacetime is described by an $SL(2,ℝ)$ matrix $p$, and the spacetime metric is $ds^2 = - (dp)$.

A Killing Vector Treatment of Multiboundary Wormholes · Review of multiboundary wormholes · 0.93

Cites as background 4 papers

The Ryu-Takayanagi proposal [ref] and its generalizations [ref] have given us important insights into the description of spacetime in holographic theories of quantum gravity.

A Covariant Holographic Entanglement Entropy Proposal · Introduction · 1.00
The Ryu-Takayanagi proposal [ref] and its generalizations [ref] have given us important insights into the description of spacetime in holographic theories of quantum gravity.

Quantum corrections to holographic entanglement entropy · Introduction · 1.00
The Ryu-Takayanagi proposal [ref] and its generalizations [ref] have given us important insights into the description of spacetime in holographic theories of quantum gravity.

Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime · Introduction · 1.00

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