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Pauli Manipulation Detection Codes and Applications to Quantum Communication over Adversarial Channels
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| Conference: | EUROCRYPT 2024 |
| Abstract: | We introduce and explicitly construct a quantum error-detection code we coin a "Pauli Manipulation Detection” code (or PMD), which detects every Pauli error with high probability. We apply them to construct the first near-optimal codes for two tasks in quantum communication over adversarial channels. Our main application is an approximate quantum code over qubits which can efficiently correct from a number of (worst-case) erasure errors approaching the quantum Singleton bound. Our construction is based on the composition of a PMD code with a stabilizer code which is list-decodable from erasures, a variant of the stabilizer list-decodable codes studied by [LS06, BGG22]. Our second application is a quantum authentication code for "qubit-wise" channels, which does not require a secret key. Remarkably, this gives an example of a task in quantum communication which is provably impossible classically. Our construction is based on a combination of PMD codes, stabilizer codes, and classical non-malleable codes [DPW09], and achieves "minimal redundancy" (rate $1-o(1)$). |
BibTeX
@inproceedings{eurocrypt-2024-33907,
title={Pauli Manipulation Detection Codes and Applications to Quantum Communication over Adversarial Channels},
publisher={Springer-Verlag},
author={Thiago Bergamaschi},
year=2024
}