International Association for Cryptologic Research

International Association
for Cryptologic Research


Thiago Bergamaschi


Pauli Manipulation Detection Codes and Applications to Quantum Communication over Adversarial Channels
Thiago Bergamaschi
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 $1-o(1)$).