An algebraic description of the Page transition

Haocheng Zhong

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arXiv · 2601.11363

An algebraic description of the Page transition

Haocheng Zhong

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Abstract

In this work, we develop an algebraic description of the Page transition, a key feature in black hole evaporation where the entropy of Hawking radiation follows a unitary Page curve instead of monotonically increasing. By applying concepts from approximate quantum error correction with complementary recovery, we characterize the Page transition as a phase transition in channel recovery. We then generalize the description to infinite-dimensional settings using algebraic relative entropy, which remains valid even in type III factors. For type I/II factors, explicit probes based on relative entropy differences are derived, serving as indicators for the transition at the Page time.

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Haocheng Zhong. 2026-01-16. An algebraic description of the Page transition. https://arxiv.org/abs/2601.11363

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