Structure Theorem for Quantum Replacer Codes
Eric Chitambar, Sarah Hagen, David W. Kribs, Mike I. Nelson, Andrew Nemec
TL;DR
This paper establishes a comprehensive structure theorem for quantum replacer codes, unifying various special cases and previous results in quantum error correction, with practical examples and new insights.
Contribution
It introduces a unifying structure theorem for quantum replacer codes, enhancing understanding and analysis of these error-correcting codes.
Findings
Theorem synthesizes various special cases of quantum replacer codes.
Provides new examples and applications of the structure theorem.
Revisits subclasses of codes from a novel perspective.
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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