Structure Theorem for Quantum Replacer Codes

• URL: http://arxiv.org/abs/2505.06659v1
• Date: Sat, 10 May 2025 14:22:31 GMT
• Title: Structure Theorem for Quantum Replacer Codes
• Authors: Eric Chitambar, Sarah Hagen, David W. Kribs, Mike I. Nelson, Andrew Nemec,
• Abstract summary: Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels.<n>We prove a structure theorem for such codes that synthesizes a variety of special cases with earlier theoretical work in quantum error correction.
• Score: 5.5807436820313345
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error correction. We prove a structure theorem for such codes that synthesizes a variety of special cases with earlier theoretical work in quantum error correction. We present several examples and applications of the theorem, including a mix of new observations and results together with some subclasses of codes revisited from this new perspective.

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