Page theorem
E590896
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Page theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6397174 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Page theorem Context triple: [Page curve, relatedTo, Page theorem]
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A.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
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B.
Teorema
Teorema is a 1968 Italian art-house drama film directed by Pier Paolo Pasolini, known for its enigmatic, allegorical exploration of sexuality, faith, and bourgeois emptiness.
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C.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
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D.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
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E.
Eliassen–Palm theorem
The Eliassen–Palm theorem is a fundamental result in atmospheric dynamics that relates wave activity and mean-flow interaction, providing a framework for understanding how atmospheric waves transport momentum and energy.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Page theorem Target entity description: The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
A.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
B.
Teorema
Teorema is a 1968 Italian art-house drama film directed by Pier Paolo Pasolini, known for its enigmatic, allegorical exploration of sexuality, faith, and bourgeois emptiness.
-
C.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
D.
Euler’s theorem
Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
-
E.
Eliassen–Palm theorem
The Eliassen–Palm theorem is a fundamental result in atmospheric dynamics that relates wave activity and mean-flow interaction, providing a framework for understanding how atmospheric waves transport momentum and energy.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
result in black hole physics
ⓘ
result in quantum information theory ⓘ theorem ⓘ |
| alsoKnownAs | Page’s average entropy theorem NERFINISHED ⓘ |
| appliesTo |
bipartite quantum systems
ⓘ
random pure states on a composite Hilbert space ⓘ |
| assumes |
Haar-random pure state on the full Hilbert space
ⓘ
finite-dimensional Hilbert spaces ⓘ |
| author | Don Page NERFINISHED ⓘ |
| characterizes | average entanglement entropy as a function of subsystem dimensions ⓘ |
| context |
discussions of information loss in black holes
ⓘ
unitary black hole evaporation models ⓘ |
| describes |
average entanglement entropy of a subsystem for a random pure state
ⓘ
typical entanglement entropy of a subsystem of a larger quantum system ⓘ |
| domain | composite Hilbert space H = H_A ⊗ H_B ⓘ |
| field |
black hole physics
ⓘ
quantum gravity ⓘ quantum information theory ⓘ |
| hasConsequence |
provides statistical basis for the Page time concept
ⓘ
supports unitary evolution in black hole evaporation scenarios ⓘ |
| implies |
entanglement entropy of the smaller subsystem is close to its maximal possible value
ⓘ
for a typical pure state the reduced density matrix of the smaller subsystem is close to maximally mixed ⓘ |
| influenced |
modern formulations of the Page curve in holography
ⓘ
quantum information approaches to black hole physics ⓘ |
| mathematicalTool |
properties of high-dimensional Hilbert spaces
ⓘ
random matrix theory ⓘ |
| namedAfter | Don Page NERFINISHED ⓘ |
| predicts |
entanglement entropy first increases and then decreases during black hole evaporation
ⓘ
entanglement entropy of a subsystem follows the Page curve in black hole evaporation models ⓘ typical entanglement entropy is nearly maximal for the smaller subsystem ⓘ |
| publication | Don N. Page, "Average entropy of a subsystem," Physical Review Letters 71, 1291 (1993) NERFINISHED ⓘ |
| relatedTo |
Haar measure on unitary group
ⓘ
Page time NERFINISHED ⓘ typicality in quantum statistical mechanics ⓘ |
| relatesConcept |
Page curve
NERFINISHED
ⓘ
black hole information paradox NERFINISHED ⓘ entanglement entropy ⓘ von Neumann entropy NERFINISHED ⓘ |
| states | for dim(H_A) ≤ dim(H_B), the average entanglement entropy of A is close to ln(dim(H_A)) ⓘ |
| supports | statistical arguments against information loss in quantum gravity ⓘ |
| usedFor |
estimating average entanglement entropy in random quantum states
ⓘ
modeling information flow in black hole evaporation ⓘ understanding typical properties of entanglement in many-body quantum systems ⓘ |
| yearProposed | 1993 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Page theorem Description of subject: The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.