Whose Page Curve? Operator Classes, Charge Reference Frames, and Information Recovery in Charge-Locked Evaporation

Mustafa Boudjerada

Published Aug 25, 2026• 0 citations

Abstract

The Page curve is the standard signature of unitary information recovery in an evaporating quantum system. This work asks a question usually left implicit: whose Page curve? In a solvable charge-locked evaporation model, the radiation observables separate into two classes: the charge-coherent algebra, available to an observer with the appropriate charge reference frame, and the charge-invariant algebra of an observer without such a reference frame. These two observers do not recover the same information curve. For the full charge-coherent algebra, the Page curve follows the standard unitary pattern: the radiation entropy rises and then returns exactly to zero, with all interior microstates becoming mutually orthogonal and perfectly decodable radiation records. For the charge-invariant algebra, the turnover is incomplete. The accessible entropy terminates at the charge-distribution entropy, representing the information deficit caused by the missing reference frame. Microstates related by a global charge-phase transformation remain indistinguishable to this observer, not because information is destroyed, but because it is inaccessible within that observable algebra. The work establishes an operator-class Page theorem: complete purification and full information recovery are properties of the charge-coherent algebra, while charge-invariant observers experience a Page curve truncated by the entropy associated with the missing charge reference frame. The model also reveals a mode-structure law. Multi-channel charged radiation can carry relative-charge information internally and locks only the global charge-phase bit, while a single effective channel can lock the full information content. An external reference frame restores accessibility only when its charge quantum matches the charge quantum of the hidden coherence, demonstrating a precise reference-frame selection rule. This work is a circuit-level quantum information model with no gravity and no dynamical backreaction. It does not claim a black-hole evaporation solution. Instead, it provides an exactly solvable framework showing how information recovery can depend on observable algebra and reference frame in systems with conserved charges. All results are accompanied by reproducibility scripts and verification procedures.

DOI: 10.5281/zenodo.22088495

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