Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels

Fuente: arXiv
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Main Author: Bergamaschi, Thiago
Format: Preprint
Published: 2023
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author Bergamaschi, Thiago
author_facet Bergamaschi, Thiago
contents We introduce and explicitly construct a quantum 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. 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 (Dziembowski et al., 2009), and achieves "minimal redundancy" (rate $1-o(1)$).
format Preprint
id arxiv_https___arxiv_org_abs_2304_06269
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels
Bergamaschi, Thiago
Quantum Physics
We introduce and explicitly construct a quantum 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. 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 (Dziembowski et al., 2009), and achieves "minimal redundancy" (rate $1-o(1)$).
title Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels
topic Quantum Physics
url https://arxiv.org/abs/2304.06269