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.
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 ⓘ |
Referenced by (1)
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