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What can we learn about islands and state paradox from quantum information theory?
High Energy Physics - Theory · Submitted 20 Jul 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that the Page curve can still be realized even if information is lost and the information paradox can be attributed to the measurement problem.
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The abstract, sentence by sentence
Recent discovery of the fine-grained entropy formula in gravity succeeded in reconstructing the Page curves that are compatible with unitary evolution. The formula of generalized entropy derived from the gravitational path integration, nevertheless, does not provide concrete insight on how the information comes out from the black hole given that the state of the radiation seems to follow what was given by Hawking. In this paper, we start from a qubit model and provide a quantum informational interpretation of entanglement islands and draw the parallel between the black hole information paradox and the problems of measurements in quantum mechanics. We show that the Page curve can still be realized even if information is lost and the information paradox can be attributed to the measurement problem. We argue that such interpretation is necessary for a quantum informational model if smooth horizons and bulk reconstruction are assumed, and show how it explains the Page curves of solvable models of 2D gravity. Though speculative, the similarities between the black hole information problem and the measurement problem may suggest some link in the origins of the two fundamental issues of distant fields.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recent discovery of the fine-grained entropy formula in gravity succeeded in reconstructing the Page curves that are compatible with unitary evolution. | background 1.00 | 0.05 | 0.04 | asserted 0.94 |
| s1 | The formula of generalized entropy derived from the gravitational path integration, nevertheless, does not provide concrete insight on how the information comes out from the black hole given that the state of the radiation seems to follow what was given by Hawking. | gap 0.85 | 0.11 | 0.03 | asserted 1.00 |
| s2 | In this paper, we start from a qubit model and provide a quantum informational interpretation of entanglement islands and draw the parallel between the black hole information paradox and the problems of measurements in quantum mechanics. | contribution 0.96 | 0.92 | 0.11 | asserted 0.98 |
| s3 | We show that the Page curve can still be realized even if information is lost and the information paradox can be attributed to the measurement problem. | result 0.85 | 0.90 | 0.69 | asserted 1.00 |
| s4 | We argue that such interpretation is necessary for a quantum informational model if smooth horizons and bulk reconstruction are assumed, and show how it explains the Page curves of solvable models of 2D gravity. | contribution 0.57 | 0.90 | 0.20 | asserted 1.00 |
| s5 | Though speculative, the similarities between the black hole information problem and the measurement problem may suggest some link in the origins of the two fundamental issues of distant fields. | interpretation 0.77 | 0.24 | 0.12 | hedged possibility 0.78 |
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The paper
Original abstract
Recent discovery of the fine-grained entropy formula in gravity succeeded in reconstructing the Page curves that are compatible with unitary evolution. The formula of generalized entropy derived from the gravitational path integration, nevertheless, does not provide concrete insight on how the information comes out from the black hole given that the state of the radiation seems to follow what was given by Hawking. In this paper, we start from a qubit model and provide a quantum informational interpretation of entanglement islands and draw the parallel between the black hole information paradox and the problems of measurements in quantum mechanics. We show that the Page curve can still be realized even if information is lost and the information paradox can be attributed to the measurement problem. We argue that such interpretation is necessary for a quantum informational model if smooth horizons and bulk reconstruction are assumed, and show how it explains the Page curves of solvable models of 2D gravity. Though speculative, the similarities between the black hole information problem and the measurement problem may suggest some link in the origins of the two fundamental issues of distant fields.
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References
How the literature uses it
7 arXiv papers cite this in 10 sentences
Papers citing it · 7 sentences without a confident label
Uses its method or tool 1 paper
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In the effective braneworld theory comprised of a cosmological spacetime coupled with a non-gravitating thermal bath, we may use the island prescription to compute the entanglement entropy for the subsystem $A$ in the thermal bath as follows [ref] [equation] As discussed in [ref] , in the effective theory the brane conformal time $τ^'$ may be treated as a natural extension of the bath time $τ$ and the island may be chosen as $I=[w_1^I,w_2^I]=[(ϕ_1,τ_0+τ_I/ℓ),(ϕ_2,τ_0+τ_I/ℓ)]$.
Reflected entropy and islands in a braneworld cosmology · Islands in cosmology · 0.93
Cites it as background 2 papers
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This in turn led to a wide range of exciting developments through the application of the island formula to a variety of black hole/bath systems and their corresponding dual $CFT$s in the context of holography [ref] .
Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors · Introduction · 0.93
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For recent related works, see [ref] .
Defect extremal surfaces for entanglement negativity · Introduction · 0.98
What it cites · 51 sentences without a confident label
Contests 1 paper
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The argument provided in [ref] has a drawback of assuming that the information is sent into the black hole before the Page time.
Cool horizons for entangled black holes · Retrospect on no-cloning theorem in black holes · contest 0.79
Compares with 5 papers
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This gives a continuous information leaking picture which is different from what Page argued [ref] .
Average Entropy of a Subsystem · Final-state projection of black holes · 0.85
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This gives a continuous information leaking picture which is different from what Page argued [ref] .
Information in Black Hole Radiation · Final-state projection of black holes · 0.85
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This is similar to the Horowitz-Maldacena (HM) proposal [ref] .
The black hole final state · Island–measurement correspondence · 0.91
Cites as support 4 papers
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As remarked in [ref] , such measurement with pre-determined results is at odds with quantum mechanics and violates causality.
Comment on "The black hole final state" · Final-state projection of black holes · 0.98
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The nonperturbative correction which looks like semi-random noise that is exponentially suppressed, gives $𝒪(1)$ corrections to the entanglement entropy of the black hole after a sufficient amount of radiations have been emitted [ref] .
An Infalling Observer in AdS/CFT · Why purification is necessary · 0.96
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The nonperturbative correction which looks like semi-random noise that is exponentially suppressed, gives $𝒪(1)$ corrections to the entanglement entropy of the black hole after a sufficient amount of radiations have been emitted [ref] .
More quantum noise from wormholes · Why purification is necessary · 0.96
Cites as background 32 papers
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The gravity/ensemble duality is a proposal that the GPI calculates an ensemble of quantum mechanical theories without gravity [ref] .
Replica wormholes and the black hole interior · Dictionary from gravity theory to quantum information · 0.94
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The gravity/ensemble duality is a proposal that the GPI calculates an ensemble of quantum mechanical theories without gravity [ref] .
Unitarity From a Smooth Horizon? · Dictionary from gravity theory to quantum information · 0.94
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The gravity/ensemble duality is a proposal that the GPI calculates an ensemble of quantum mechanical theories without gravity [ref] .
Eigenstate Thermalization and Disorder Averaging in Gravity · Dictionary from gravity theory to quantum information · 0.94
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