Black Hole Radiation Decoding in the Haar Random Oracle Model

Abstract:We prove 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 with any constant Haar-averaged advantage over trivial decoding requires queries proportional to the Hilbert-space dimension of the remaining black hole. The lower bound is unconditional for decoders chosen independently of the sampled unitary, allows arbitrary computation between queries, and access to $U, U^\dagger, U^*, U^\mathsf T$ along with the controlled variants. An existing decoder using only forward and inverse queries attains a matching bound. The proof uses a path recording oracle to compare real and maximally mixed states. As applications, we obtain an efficiently preparable, statistically far, computationally indistinguishable (EFI) pair and quantum commitments relative to a public Haar oracle, as well as prove a tight linear rank lower bound for Uhlmann transformation on a fixed-target family.

Quantum Physics (quant-ph); Computational Complexity (cs.CC); Cryptography and Security (cs.CR)

arXiv:2610.07124 [quant-ph]

(or arXiv:2610.07124v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.07124 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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