The Page Transition in the Multi-Time Correlations of Hawking Radiation
Abstract
The Page curve and the island formula describe a reorganization of quantum information in Hawking radiation across the Page time. We study how this reorganization appears in correlations among emissions collected at several retarded times. The late radiation is treated as a covariant multi-time process, or process tensor, and Οisland=π©β βπ©R measures the temporal memory removed when the early radiation register R is supplied. Operationally, this quantity is the corresponding change in the optimal distinguishability of the radiation process from a Markovian reference. We exhibit evaporation processes whose single-bin states and all process marginals below a finite order kββ₯ 3 remain fixed and coincide with a CP-divisible reference, while Οisland changes by order one at order kβ. The Page transition can therefore appear as a transition in the Markov order of the radiation process. When the interior mediates the late-time memory, entanglement-wedge reconstruction of the predictive interior from R Markovianizes the late process; conversely, when the late process has a minimal predictive memory and its future-affecting information is mediated by that memory, Markovianization by R supplies a simulator of its influence. A Hayden--Preskill evaporation comb and an evaporating-JT calculation realize this mechanism. The late radiation retains temporal memory across the transition, while the early radiation becomes sufficient for predicting its future multi-time statistics.
Related
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BibTeX
@misc{waghmare2026page,
title = {{The Page Transition in the Multi-Time Correlations of Hawking Radiation}},
author = {Tushar Waghmare},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20456},
eprint = {2609.20456},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20456},
}
RIS
TY - UNPB
TI - The Page Transition in the Multi-Time Correlations of Hawking Radiation
AU - Tushar Waghmare
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20456
UR - https://arxiv.org/abs/2609.20456
AB - The Page curve and the island formula describe a reorganization of quantum information in Hawking radiation across the Page time. We study how this reorganization appears in correlations among emissions collected at several retarded times. The late radiation is treated as a covariant multi-time process, or process tensor, and Ο_island=π©_β
βπ©_R measures the temporal memory removed when the early radiation register R is supplied. Operationally, this quantity is the corresponding change in the optimal distinguishability of the radiation process from a Markovian reference. We exhibit evaporation processes whose single-bin states and all process marginals below a finite order k_ββ₯ 3 remain fixed and coincide with a CP-divisible reference, while Ο_island changes by order one at order k_β. The Page transition can therefore appear as a transition in the Markov order of the radiation process. When the interior mediates the late-time memory, entanglement-wedge reconstruction of the predictive interior from R Markovianizes the late process; conversely, when the late process has a minimal predictive memory and its future-affecting information is mediated by that memory, Markovianization by R supplies a simulator of its influence. A Hayden--Preskill evaporation comb and an evaporating-JT calculation realize this mechanism. The late radiation retains temporal memory across the transition, while the early radiation becomes sufficient for predicting its future multi-time statistics.
ER -