Gravity describes the shape and behavior of spacetime; quantum theory describes states, measurements and correlations. In holographic theories, a precise relationship between quantum entanglement on a boundary and the geometry of a gravitational space behind it gives researchers a way to connect those descriptions. The best-known example is the Ryu–Takayanagi relation, which turns the entanglement entropy of a boundary region into the area of a corresponding surface in the bulk. This is a powerful result within particular mathematical models—not experimental proof that gravity in our universe is made of entanglement.
What does quantum information have to do with gravity?
At first glance, the subjects seem to describe different things. General relativity treats gravity as geometry: matter and energy shape spacetime, and that geometry influences how matter moves. Quantum theory describes physical systems through quantum states, including correlations between parts of a system that cannot be captured by assigning each part an independent state.
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Holographic theories connect the two languages. In a specified class of models, information in a nongravitational quantum theory can describe a gravitational space with one more dimension. Within that correspondence, the pattern of quantum entanglement among boundary degrees of freedom is related to geometric features of the gravitational bulk. That relationship gives researchers a way to ask how bulk geometry can be encoded in quantum information, and how gravity might arise from a more fundamental description.
The careful wording matters. The holographic correspondence is a mathematical framework, and results derived within it can be exact and highly informative. But a result about a holographic model is not by itself evidence that our observed universe has that same description. “Spacetime is made of entanglement” is a useful motivating slogan, not an established literal account of the universe.
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AdS/CFT: the setting where the connection is precise
The most developed setting is the AdS/CFT correspondence. On one side is a gravitational theory in an anti-de Sitter (AdS) bulk. On the other is a conformal field theory (CFT), a quantum field theory living on the bulk’s boundary. The proposal is that the two descriptions are equivalent: they describe the same underlying physics in different terms.
A hologram offers a rough analogy: information represented on a lower-dimensional surface can encode a higher-dimensional description. But AdS/CFT is more precise than an ordinary optical hologram. It specifies a relationship between theories, not a claim that a familiar physical object is projected into space. Researchers can use the boundary theory’s quantum properties to investigate the gravitational bulk, and can use the bulk description to understand features of the boundary theory.
This setting is useful because it gives a controlled place to study questions that are difficult in quantum gravity, including how bulk geometry is encoded and how information behaves in systems involving black holes. The conclusions are strongest when they stay within the assumptions and models where the duality applies.
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Entanglement is a kind of quantum correlation between subsystems. If a system is divided into a region A and everything outside it, the state of A may not fully describe the correlations between A and its surroundings. Entanglement entropy is a measure of how much information is entangled across that division. It depends on the quantum state and on where the division is made.
The Ryu–Takayanagi (RT) prescription makes this quantity geometric in a static, classical bulk setting. For a boundary region A, it says:
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S(A) = Area(γA) / (4GN)
Here, S(A) is the entanglement entropy of A; γA is a minimal bulk surface anchored to the boundary of A; Area(γA) is that surface’s area; and GN is Newton’s constant. The relation is not a statement that entropy and area are interchangeable in every physical system. It is a prescription within the relevant holographic setting, with the stated classical and static qualifications.
The anchoring condition links the boundary region to the bulk: the surface ends at the boundary of A. To find the area used by the prescription, one considers bulk surfaces with that anchoring and selects a minimal one. The entanglement entropy calculated in the boundary theory is then related to the area of that bulk surface. Thus a quantum-information measure in one description yields geometric data in the other.
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The original proposal was submitted on February 28, 2006. Its worked example considered a two-dimensional conformal field theory with an AdS3 dual and reproduced the known CFT entanglement entropy. That example is an important anchor: the relation was not merely a visual metaphor, but a quantitative agreement in a specified holographic case.
How entanglement can constrain bulk geometry
The RT relation suggests a way to reason from boundary information to bulk shape. If the boundary state changes, its entanglement across a chosen region can change. In the holographic description, the area associated with the corresponding bulk surface must reflect that change. Considering entanglement for different boundary regions therefore supplies geometric constraints, rather than just a single area measurement.
One can picture this as asking many related questions: what is the entropy of this boundary region, and what about a nearby or larger region? Each answer is associated with a surface in the bulk. The collection of those surface areas and arrangements encodes information about the geometry. This is why entanglement can serve as a diagnostic for studying the bulk and its reconstruction from boundary data.
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That does not mean entanglement alone has already been shown to determine every feature of every gravitational spacetime. The prescription provides a precise dictionary in holographic models, while the broader question of how much geometry can be recovered, and under what conditions, is part of ongoing theoretical work.
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What tensor networks add—and what they do not
Tensor networks provide a discrete way to represent quantum states and their patterns of entanglement. A network is built from connected mathematical objects, with the pattern of connections helping to track how information is distributed among subsystems. In some models, the network can be drawn in a way that resembles a geometry: network structure represents entanglement relationships, while the diagram offers a visual intuition for a candidate bulk space.
This makes tensor networks useful as models and explanatory tools. They help researchers think about how an arrangement of quantum correlations might correspond to a bulk-like structure, and how changing the entanglement pattern could affect that structure. They are not, simply by being drawable as a geometry, a complete description of holography or a literal map of the universe.
Reviews of the subject identify an important limitation: it remains unclear whether tensor networks reproduce all information-theoretic aspects of holography beyond extremal-surface entropy. The broader relationship between tensor networks and gravity remains a research question. Their value is therefore partly conceptual and model-building: they make certain features easier to see without settling the full theory.
Quantum error correction and the puzzle of bulk reconstruction
Quantum error correction offers a more formal way to understand how bulk information can be represented on a boundary. In ordinary error-correcting codes, information is encoded redundantly so that it can still be recovered even if part of the code is unavailable. Holographic quantum-error-correction frameworks use a related idea to describe how bulk information can be encoded across boundary degrees of freedom.
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Redundancy helps explain why information about a bulk region need not be stored in just one small boundary piece. In these frameworks, information about the bulk can be reconstructed from appropriate boundary subregions. This offers a language for asking which boundary data are sufficient to recover a given bulk feature, and how locality in the bulk can coexist with an encoding distributed over the boundary.
The associated idea of an entanglement wedge identifies a bulk region connected to a boundary region for purposes of holographic reconstruction. Entanglement-wedge reconstruction describes how information in that bulk region can be recovered from the corresponding boundary degrees of freedom. This extends the discussion beyond a simple one-to-one picture in which each point in the bulk has one unique boundary address.
Quantum error correction is an interpretation supported by formal frameworks and toy models, not experimental evidence that the universe itself is a quantum code. Its contribution is explanatory: it clarifies how bulk information could be robustly encoded and reconstructed in a holographic description.
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RT surfaces, tensor networks and quantum error correction are related tools within the holographic research program, not competing theories that must be chosen between. Each illuminates a different part of the problem.
| Framework | What it helps explain | How literally to read it |
|---|---|---|
| RT relation and quantum extremal surfaces | Connect boundary entanglement entropy to a bulk surface’s area. Quantum extremal surfaces extend the classical area prescription by adding quantum corrections. | A quantitative prescription in the relevant holographic setting; the classical RT statement is specifically for a static classical bulk. |
| Tensor networks | Represent patterns of entanglement in a discrete network and provide visual intuition for candidate geometry. | A useful model and visualization, not an established complete account of holography or gravity. |
| Quantum error correction and entanglement wedges | Describe redundant encoding of bulk information and reconstruction from boundary subregions. | A formal language supported by frameworks and toy models, not a measured property of our universe. |
Quantum extremal surfaces matter because the classical area-only formula is not the whole story once quantum corrections are considered. The broader review literature also discusses the JLMS relation, entanglement wedges, and connections between bulk canonical energy and boundary Fisher information. Together, these ideas show that the information–geometry connection extends beyond one entropy formula, while remaining a technical program with specific assumptions and open questions.
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What this approach helps researchers investigate
One application is bulk reconstruction: understanding how much of a gravitational interior can be inferred from boundary quantum data, and which boundary regions carry information about which bulk regions. Entanglement-wedge reconstruction and quantum-error-correction ideas provide tools for framing that problem.
Another is the study of black-hole information. Holography offers a setting in which gravitational questions can be translated into quantum-theory language, so researchers can examine how information is encoded and how quantum correlations relate to bulk descriptions. This is a reason the framework is influential; it does not mean that every black-hole question has been resolved.
More broadly, the program tests whether geometric features can emerge from properties of a quantum state rather than being treated as fundamental inputs. The RT relation makes that question concrete by tying a boundary entropy to a bulk area. Related tools investigate how the encoding works, which regions are reconstructible and what kinds of quantum corrections must be included.
What the results do not establish
- They do not show experimentally that gravity in the observed universe emerges from entanglement.
- They do not establish that all spacetimes, or the cosmology of our universe, have the AdS/CFT description.
- They do not make “spacetime is made of entanglement” a literal, universally proven statement.
- They do not show that tensor networks already capture every information-theoretic feature of holography.
- They do not make classical RT’s area prescription applicable without qualification to quantum or time-dependent situations; extensions such as quantum extremal surfaces address corrections beyond that classical prescription.
These limits do not diminish the mathematical results. They distinguish what has been established inside a controlled holographic framework from the larger claim that the same mechanism explains gravity in our physical universe.
Why the question remains open
The field is active rather than finished. In a 2025 Physical Review Letters essay, physicist Tadashi Takayanagi surveyed progress and open problems in emergent holographic spacetime from quantum information. He wrote that “quantum information theory offers crucial hints” for understanding how gravity emerges from quantum field theories within holography. The qualification “within holography” is central: the work develops powerful tools and clues in that framework, but does not claim experimental confirmation of an entanglement origin for gravity in our universe.
The most accurate takeaway is therefore both ambitious and bounded. In AdS/CFT, entanglement is quantitatively connected to bulk geometry, and tensor networks and quantum error correction help researchers investigate how that geometry is represented and reconstructed. Whether those insights amount to a full explanation of gravity in the real universe remains unresolved.
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