Quantum

Black Hole Radiation Decoding in the Haar Random Oracle Model

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Briefings

A 2026 arXiv preprint establishes optimal query bounds for recovering a single qubit from black-hole radiation in the Haar random oracle model, provided the remaining black hole holds at most one-sixteenth of the system's qubits. The proof is unconditional for decoders independent of the sampled unitary, allowing arbitrary computation between queries and access to unitary operations along with controlled variants. An existing decoder using only forward and inverse queries achieves this matching bound. The work yields an efficiently preparable, statistically far, and computationally indistinguishable pair relative to a public Haar oracle, alongside a tight linear rank lower bound for Uhlmann transformation on a fixed-target family.

Key points

• The paper proves optimal query bounds for recovering a single qubit from black-hole radiation in the Haar random oracle model when the remaining black hole contains at most one-sixteenth of the system's qubits.
• Recovery requires queries proportional to the Hilbert-space dimension of the remaining black hole, and the lower bound is unconditional for decoders chosen independently of the sampled unitary.

Context and limitations

The results apply only to the Haar random oracle model with a specific constraint on the remaining black hole's qubit count; the paper does not address other oracle models or different qubit distributions.

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