Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2112.02044 · AIP conference proceedings

Euclidean path integral, entanglement entropy, and quantum boundary conditions

Dong-han Yeom

Published Jan 1, 2024• 0 citations
arXivHTMLPDF

Abstract

To understand the information loss paradox in a consistent way, we provide a brief big picture that describes both outside and inside a black hole. We summary several ideas including the Euclidean path integral, the entanglement entropy, and the quantum gravitational treatment for the singularity. This integrated discussion can provide an alternative point of view toward the ultimate resolution of the information loss paradox.

DOI
10.1063/5.0216044

Related papers

The Black Hole Information Paradox: Is Omniscience a Fundamental Property of the Universe?

Jabi Elijah Shriki

We seek to examine the ontological aspects of the resolution of the black hole information paradox. Several concepts which are now central to our understanding of quantum mechanics arose from our resolution to this paradox, and these concepts point to the conservation of all information, even on a quantum level. If quantum information is conserved and can never be erased or destroyed, then this indicates that all information is at least theoretically, ultimately retrievable and knowable from the event horizon of the universe. Ontologically, this supports the contention that a repository of all information in the universe must therefore exist. Herein, we trace the steps in this contention and conclude with the argument that our understanding of the universe points to the existence of an omniscient entity.

International Journal of Religion•Sep 21, 2024•0 citations

Complexity and Entanglement in Quantum Gravity

Arjun Kar

We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface.

•Jan 1, 2020•0 citations

Is there truly classical information?

Andrei T. Patrascu

All entropy is entanglement entropy. This appears as the result of the existence of black holes. The origin of entropy and the way in which it defines the perceived time direction in macroscopic systems has been discussed and can be debated as long as one ignores black holes. In such a case, thermodynamic entropy may define the arrow of time and entanglement entropy defines some special globally defined entropy encoding information in a non-local sense. With black holes however, if we accept that in-falling objects must have their information encoded outside, for example through non-local fluctuations away from thermalisation of the Hawking radiation, and that the horizon of a black hole cuts all classical information from the outside, then all the entropy that can be added to the black hole, which is basically any form of entropy, must be translated into some form of entanglement entropy to be detected outside. A discussion about the nature of information channels shows that spacetime may not be a correlation-insensitive channel as usually employed in the engineering of quantum computing. Time may emerge as a property of the complexity of entanglement spreading.

arXiv:2209.02587•Aug 4, 2022•0 citations

Black holes and quantum entanglement

Ro Jefferson

The black hole information paradox is a contradiction between fundamental principles which has puzzled physicists for over forty years. The crux of the problem lies in an assumption about the structure of entanglement across the event horizon, namely, that the Hilbert space factorizes. While valid in quantum mechanics, this fails drastically in quantum field theory, and hence a deeper understanding of entanglement is required if further progress is to be made. Recently, ideas from algebraic quantum field theory have provided new insight into this issue, and show promise for elucidating the connection between entropy and horizons that underlies black hole thermodynamics.

arXiv:1901.01149•Jan 2, 2019•7 citations

The Black Hole Information Paradox as Projection Boundary: Ω-Conservation, Event Horizons, and the Non-Destruction of Information

Vinness Aisingioro Ollervides

Abstract The black hole information paradox (Hawking, 19741976) poses a fundamental conict: quantum mechanics requires unitary evolution (information is preserved), while black hole evaporation via Hawking radiation appears to destroy information (the radiation is thermal, carrying no information about the in-fallen state). After fty years of debate, the paradox remains unresolvedHawking conceded it in 2004 [3] but no complete mechanism has been identied. ˆ We resolve the paradox by identifying its source: confusing Ω with Πext[Ω]. Information is never destroyed. Ω-conservation (Noether, P2) guarantees this. What is destroyed at the event horizon is not the information but the exterior ˆ observer's projection operator : Πext becomes inapplicable inside the horizon. The ˆ ˆ information encoded in the in-fallen matter passes from Πext[Ω] to Πint[Ω]two projections of the same Ω = 1 that agree in total but disagree in local accessibility. Hawking radiation is the κ→0 leakage of Ω-entanglement across the projection boundary. The Page curve [4]entanglement entropy rising and then falling as the black hole evaporatesfollows directly from Ω-conservation without invoking island formulas [8, 9] or specic stringy mechanisms. The paradox is not a paradox. It is a projection error.

•Mar 5, 2026•0 citations

4 The Black Hole Information Paradox and the Collapse of the Wave Function

Elias Okon, Daniel Sudarsky

The black hole information paradox arises from an apparent conflict between the Hawk-ing black hole radiation and the fact that time evolution in quantum mechanics is unitary. The trouble is that while the former suggests that information of a system falling into a black hole disappears, the latter implies that information must be con-served. In this work we discuss the current divergence in views regarding the paradox, we evaluate the role that objective collapse theories could play in its resolution and we propose a link between spontaneous collapse events and microscopic virtual black holes. 1

•Feb 14, 2015•15 citations
To understand the information loss paradox in a consistent way, we provide a brief big picture that describes both outside and inside a black hole. We summary several ideas including the Euclidean path integral, the entanglement entropy, and the quantum gravitational treatment for the singularity. This integrated discussion can provide an alternative point of view toward the ultimate resolution of the information loss paradox.
We seek to examine the ontological aspects of the resolution of the black hole information paradox. Several concepts which are now central to our understanding of quantum mechanics arose from our resolution to this paradox, and these concepts point to the conservation of all information, even on a quantum level. If quantum information is conserved and can never be erased or destroyed, then this indicates that all information is at least theoretically, ultimately retrievable and knowable from the event horizon of the universe. Ontologically, this supports the contention that a repository of all information in the universe must therefore exist. Herein, we trace the steps in this contention and conclude with the argument that our understanding of the universe points to the existence of an omniscient entity.
We present a collection of recent results concerning quantum information theory applied to quantum gravity. We first study the entanglement structure of Euclidean path integral states in SU(2) Chern-Simons theory, where we elucidate a connection between topological entanglement and quantum mechanical entanglement. We prove that the topology of certain three-manifolds controls the entanglement structure of the resulting quantum state, and conjecture a more general relationship for arbitrary three-manifolds. We then analyze the quantum circuit complexity of the time evolution operator in the Sachdev-Ye-Kitaev model, a theory of near-extremal black hole microstates. We find that this complexity grows linearly for a time exponential in the entropy, modulo a caveat concerning global obstructions to the growth of the distance function along geodesics, which we do not rule out. This constitutes a partial proof of Susskind’s conjecture about the complexity growth of black holes. Finally, we address the black hole information paradox in three dimensions by considering a toy model of black hole microstates in the form of an end-of-the-world brane. This brane carries a quantum theory which is itself holographic, and we compute entanglement entropies in the glued dual geometry by using a Ryu-Takayanagi formula where the minimal entropy surface can pass through the gluing surface.
All entropy is entanglement entropy. This appears as the result of the existence of black holes. The origin of entropy and the way in which it defines the perceived time direction in macroscopic systems has been discussed and can be debated as long as one ignores black holes. In such a case, thermodynamic entropy may define the arrow of time and entanglement entropy defines some special globally defined entropy encoding information in a non-local sense. With black holes however, if we accept that in-falling objects must have their information encoded outside, for example through non-local fluctuations away from thermalisation of the Hawking radiation, and that the horizon of a black hole cuts all classical information from the outside, then all the entropy that can be added to the black hole, which is basically any form of entropy, must be translated into some form of entanglement entropy to be detected outside. A discussion about the nature of information channels shows that spacetime may not be a correlation-insensitive channel as usually employed in the engineering of quantum computing. Time may emerge as a property of the complexity of entanglement spreading.
The black hole information paradox is a contradiction between fundamental principles which has puzzled physicists for over forty years. The crux of the problem lies in an assumption about the structure of entanglement across the event horizon, namely, that the Hilbert space factorizes. While valid in quantum mechanics, this fails drastically in quantum field theory, and hence a deeper understanding of entanglement is required if further progress is to be made. Recently, ideas from algebraic quantum field theory have provided new insight into this issue, and show promise for elucidating the connection between entropy and horizons that underlies black hole thermodynamics.
Abstract The black hole information paradox (Hawking, 19741976) poses a fundamental conict: quantum mechanics requires unitary evolution (information is preserved), while black hole evaporation via Hawking radiation appears to destroy information (the radiation is thermal, carrying no information about the in-fallen state). After fty years of debate, the paradox remains unresolvedHawking conceded it in 2004 [3] but no complete mechanism has been identied. ˆ We resolve the paradox by identifying its source: confusing Ω with Πext[Ω]. Information is never destroyed. Ω-conservation (Noether, P2) guarantees this. What is destroyed at the event horizon is not the information but the exterior ˆ observer's projection operator : Πext becomes inapplicable inside the horizon. The ˆ ˆ information encoded in the in-fallen matter passes from Πext[Ω] to Πint[Ω]two projections of the same Ω = 1 that agree in total but disagree in local accessibility. Hawking radiation is the κ→0 leakage of Ω-entanglement across the projection boundary. The Page curve [4]entanglement entropy rising and then falling as the black hole evaporatesfollows directly from Ω-conservation without invoking island formulas [8, 9] or specic stringy mechanisms. The paradox is not a paradox. It is a projection error.
The black hole information paradox arises from an apparent conflict between the Hawk-ing black hole radiation and the fact that time evolution in quantum mechanics is unitary. The trouble is that while the former suggests that information of a system falling into a black hole disappears, the latter implies that information must be con-served. In this work we discuss the current divergence in views regarding the paradox, we evaluate the role that objective collapse theories could play in its resolution and we propose a link between spontaneous collapse events and microscopic virtual black holes. 1