# Toy Model for Black Hole Decoherence
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**Anchor paper:** K. Agarwal, N. Bao, "Toy model for decoherence in the black hole information problem," *Phys. Rev. D* 102, 086017 (2020). [arXiv:1912.09491]
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## Background
When a black hole evaporates via Hawking radiation, the outgoing radiation appears thermal and uncorrelated with what fell in, seemingly destroying information — the black hole information paradox. The AMPS "firewall" argument sharpened this: unitarity requires late Hawking quanta maximally entangled with early radiation, while a smooth horizon requires them maximally entangled with the interior, violating monogamy of entanglement. One proposed resolution is that decoherence — entanglement of Hawking quanta with an inaccessible bath (e.g. graviton fluctuations) — hides the monogamy violation from infalling observers. What was missing was a concrete, calculable model of this decoherence mechanism, since full quantum-gravity treatment is intractable.
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## New results
The authors build a solvable toy model: qubits represent the black hole interior and radiation, random Clifford gates scramble information inside a horizon shrinking by v qubits per time step, while qubits outside undergo probabilistic projective measurements (rate p) modeling bath decoherence. Tracking mutual information between early and late radiation, they found the information-paradox signature (monogamy violation) only becomes manifest once the black hole shrinks to a critical, decoherence-set size N_BH^c ≈ v/p, independent of initial size. Mapping v and p onto plausible graviton-decoherence rates via dimensional analysis, they argued this critical size is Planckian — the paradox becomes sharp only where quantum gravity was already expected to take over, without requiring the hole to store extensive information.
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![Toy model of black hole decoherence](https://ar5iv.labs.arxiv.org/html/1912.09491/assets/mainfig.svg)
*Fig. 1 — the decoherence "branching" of the wavefunction (a), the stabilizer-circuit toy model with random Clifford gates inside a shrinking horizon and probabilistic measurements outside (b), and mutual information vs. time (c).*
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## Related work in this direction
Co-author Ning Bao also collaborates with Agarwal on the later classical-shadow-tomography work (arXiv:2311.10137 / PRL 133, 130803) — a very different physical setting (black hole horizons vs. practical quantum tomography), but both turn on the same underlying question: how much information about a quantum system survives noise/decoherence, formalized with related tools (stabilizer/Clifford circuits, mutual information).
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# Parents
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* Classical Shadow Tomography & Quantum Learning⏎