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In holographic theories, quantum information—especially entanglement—can encode precise clues about the geometry of a gravitational spacetime. The Ryu–Takayanagi relation makes that connection quantitative: in a specified static, classical setting, the entanglement entropy of a region in a boundary quantum field theory is related to the area of a corresponding minimal surface in the gravitational bulk. This is a powerful framework for studying gravity, not proof that entanglement creates gravity in our universe.
Why connect quantum information with gravity?
Gravity is usually described through the geometry of spacetime: matter and energy affect that geometry, and the geometry shapes how matter moves. Quantum theory, by contrast, describes states and the relationships among parts of a system. A deep theoretical question is whether some features that look geometric from a gravitational perspective can be represented by relationships among quantum degrees of freedom.
Entanglement is a natural place to look. Two parts of a quantum system are entangled when their joint state cannot be fully described by treating each part independently. The correlations between them can be present even when the parts are considered as separate subsystems. In holographic models, those boundary correlations are related to geometric features in an additional, gravitational description.
The key qualification is the setting. The best-defined examples arise in holographic dualities, especially AdS/CFT. Within such a duality, the two descriptions are mathematically equivalent; the entanglement-to-geometry connection is not a general claim that every quantum system, or the observed universe, has already been shown to work this way.
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What AdS/CFT says
AdS/CFT is a holographic duality between a gravitational theory in an anti-de Sitter (AdS) bulk and a nongravitational conformal field theory (CFT) on the bulk’s boundary. “Bulk” means the higher-dimensional gravitational description; “boundary” means the lower-dimensional surface on which the CFT is defined. Holography here means that the boundary theory can encode a description equivalent to the bulk theory, not that the bulk is a projected image in the everyday sense.
This is a useful laboratory for questions about quantum gravity because it gives researchers two ways to describe the same theoretical system. The boundary account uses quantum-field-theory concepts, while the bulk account uses gravity and geometry. If a quantity in the boundary theory can be related to a geometric quantity in the bulk, that relation provides a concrete dictionary between the descriptions.
AdS/CFT is a specific theoretical framework, not a demonstrated model of our entire universe. The foundational Ryu–Takayanagi paper, submitted on February 28, 2006, proposed a general connection and worked through an example involving a two-dimensional CFT with an AdS3 dual. That example reproduced the known CFT entanglement entropy. Its success is important evidence for the duality’s internal structure, but it is not an experimental observation of spacetime emerging from entanglement.
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What entanglement entropy measures
To discuss entanglement in a field theory, first divide its degrees of freedom into a region A and the rest of the system. The entanglement entropy of A quantifies how much information about A is shared with its complement in the quantum state. It is a property of the state and the chosen division, rather than a measure of the region’s physical size by itself.
That distinction matters for the holographic connection. In ordinary geometry, the area of a surface is a spatial measurement. In quantum information, entanglement entropy characterizes correlations across a division. The Ryu–Takayanagi prescription links these different kinds of quantities for a particular class of holographic settings. It does not say that entropy and area mean the same thing in every context.
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The Ryu–Takayanagi formula: entropy from area
In a static, classical bulk setting, the Ryu–Takayanagi (RT) prescription calculates the entanglement entropy of a boundary region A from the area of a minimal bulk surface, γA, anchored to the boundary of A:
S(A) = Area(γA) / (4GN)
Here, S(A) is the boundary region’s entanglement entropy, Area(γA) is the area of the corresponding minimal surface in the bulk, and GN is Newton’s constant. The factor of 4GN converts the geometric area into the entropy quantity in the prescription. In this formula, “minimal” refers to the surface of least area among the relevant surfaces satisfying the boundary condition; the surface is not an arbitrary geometric feature.
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The original proposal established the formula in its stated holographic framework, including the AdS3/CFT2 worked example. It should not be applied without qualification to every gravitational situation. The formula above is the classical, static prescription; later developments address settings and corrections beyond that simple case.
How entanglement can encode geometric information
One useful way to think about the RT relation is as a map from many boundary-region entropy measurements to geometric constraints. A single region’s entropy is associated with a surface area. Considering different regions probes different surfaces, so a collection of entanglement data can provide information about the arrangement and areas of bulk surfaces.
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This is more precise than saying simply that “spacetime is made of entanglement.” That phrase captures an intuition: changing the pattern of entanglement is associated with changes in geometric structure in holographic models. But the literal slogan goes beyond what the relation alone establishes. The RT prescription provides a specific entropy-to-area dictionary under stated assumptions; it does not, by itself, derive every feature of spacetime or establish that entanglement is the universal substance of the physical universe.
The connection is useful to researchers because it lets quantum-information tools address gravitational questions. It supplies ways to calculate holographic entropies, investigate bulk reconstruction, and study questions related to black-hole information. These are applications within the theoretical framework, not evidence that all those questions have been solved.
What tensor networks add—and what they do not
A tensor network is a way of representing a complicated quantum state by connecting simpler pieces in a network. The network’s structure can represent patterns of entanglement: the links and connections indicate how parts of the state are related. In some models, the network can also be read geometrically, making it easier to visualize how a pattern of quantum correlations might correspond to a bulk-like structure.
This makes tensor networks valuable as intuition and as models for exploring entanglement and geometry. They give a discrete picture of an idea that can otherwise be mathematically abstract: the organization of quantum correlations may carry information that has a geometric interpretation. They also help researchers think about how boundary data might encode a higher-dimensional description.
A tensor-network picture is not automatically a complete model of holography. Reviews of the subject note that it remains unclear whether tensor networks reproduce all information-theoretic aspects of holography beyond extremal-surface entropy. The broader relation between tensor networks and gravity remains an open research question. A diagram that resembles a geometry is therefore a useful model, not proof that physical spacetime literally consists of that network.
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Quantum error correction and reconstructing the bulk
Quantum error correction offers a more formal way to understand how information about a bulk region could be encoded in a boundary theory. In an error-correcting code, information is stored redundantly so that it can remain recoverable even if some parts of the encoding are unavailable. Holographic quantum-error-correction frameworks use this kind of redundancy to describe how bulk information can be represented across boundary degrees of freedom.
This perspective helps address a puzzle: how can a bulk region have a meaningful description if the boundary theory is its equivalent account? In these frameworks, a piece of bulk information need not be stored in only one boundary location. Instead, it can be encoded in a way that allows reconstruction from appropriate boundary subregions. The same information may have multiple boundary representations, consistent with the idea of redundant encoding.
Entanglement-wedge reconstruction makes this idea more specific. An entanglement wedge is a bulk region associated with a chosen boundary region in holographic descriptions. The reconstruction framework relates which bulk information can be recovered to the boundary region and its entanglement structure. This supplies a formal language for discussing how bulk locality—the ability to describe bulk information as belonging to particular regions—can coexist with encoding in the boundary theory.
These ideas are part of a formal theoretical program supported by frameworks and toy models. They do not show that the universe has experimentally been found to be a quantum error-correcting code. The code analogy explains a structure in holographic models; it should not be mistaken for a direct measurement of the microscopic construction of our cosmos.
How the main ideas fit together
| Framework or tool | What it contributes | How literally to interpret it |
|---|---|---|
| RT prescription | A quantitative relation between boundary entanglement entropy and the area of a corresponding minimal bulk surface in the static classical setting. | A precise prescription within specified holographic models, not a universal entropy-area rule for all systems. |
| Quantum extremal surfaces | An extension that adds quantum corrections to the classical area prescription for holographic entropy calculations. | A development of the entropy-to-geometry framework; it does not make the classical RT formula valid without qualifications in every setting. |
| Tensor networks | A discrete and visual model for patterns of entanglement that can be interpreted geometrically. | Useful intuition and a research tool, but not established as a complete description of all information-theoretic aspects of holography. |
| Quantum error correction and entanglement wedges | A formal account of redundant bulk-information encoding and reconstruction from boundary regions. | A framework for understanding holographic encoding, not experimental evidence that our universe is a quantum code. |
These are related tools and interpretations within the holographic research program, not competing theories that require choosing only one. RT gives a clear entropy-to-area relation; quantum extremal surfaces extend the entropy calculation; tensor networks provide models and visual intuition; and error-correction ideas explain aspects of encoding and reconstruction. Each addresses a different part of the broader question of how a gravitational bulk can be represented by boundary quantum information.
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What this framework can explain—and what remains open
The robust claim is conditional: in holographic models, entanglement provides a way to encode and study bulk geometry. The RT relation is a sharp example of this correspondence, and related work extends the discussion to quantum corrections and reconstruction. The framework is valuable precisely because it makes parts of the connection calculable rather than merely metaphorical.
But it does not amount to a completed general explanation of gravity. A 2025 Physical Review Letters essay by Tadashi Takayanagi, published June 20, 2025, surveys progress and open problems in emergent holographic spacetime from quantum information. Takayanagi describes the developments as offering “crucial hints” for understanding how gravity emerges from quantum field theories within holography. That phrasing captures the field’s promise while keeping the scope clear: the account concerns gravity emerging within a holographic framework.
No experimental confirmation establishes that gravity in our observed universe emerges from entanglement. Nor do the tools discussed here establish that spacetime is literally built from qubits. The open challenge is to understand how far these holographic insights extend, whether models such as tensor networks capture more than particular features, and how the theoretical picture relates to physical gravity beyond the settings where the duality is defined.
Further reading for the technical details
Readers who want to follow the derivations can start with the foundational Ryu–Takayanagi paper and the review literature on holographic entanglement entropy. Reviews also discuss quantum extremal surfaces, entanglement wedges, the JLMS relation, and connections between bulk canonical energy and boundary Fisher information. These topics deepen the technical dictionary between boundary quantum information and bulk gravitational structure, but they do not change the central qualification: the strongest results belong to holographic settings.
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