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

• URL: http://arxiv.org/abs/2304.06269v2
• Date: Wed, 12 Jun 2024 06:00:12 GMT
• Title: Pauli Manipulation Detection codes and Applications to Quantum Communication over Adversarial Channels
• Authors: Thiago Bergamaschi,
• Abstract summary: 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.
• Score: 0.08702432681310403
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $1-o(1)$).

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