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.

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Page theorem canonical 1

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Predicate Object
instanceOf result in black hole physics ⓘ
result in quantum information theory ⓘ
theorem ⓘ
alsoKnownAs Page’s average entropy theorem ⓘ
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 ⓘ
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 ⓘ
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) ⓘ
relatedTo Haar measure on unitary group ⓘ
Page time ⓘ
typicality in quantum statistical mechanics ⓘ
relatesConcept Page curve ⓘ
black hole information paradox ⓘ
entanglement entropy ⓘ
von Neumann entropy ⓘ
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 ⓘ

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Page curve → relatedTo → Page theorem ⓘ