Problem
Research questions and friction points this paper is trying to address.
Quantum Error-Correcting Codes
Erasures
Observables
Qudits
Repair Group
Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery
🤖 AI Summary
本文提出一种线性代数方法，用于减少量子纠错码中观测值和测量的量子比特数量，以纠正给定的擦除错误，适用于一般纠缠辅助或非辅助量子纠错码。
📝 Abstract
For a general entanglement-assisted or unassisted quantum error-correcting code, a set of erasures, and an associated repair group, we propose a linear algebraic procedure to compute a reduced set of observables and a reduced repair group of codeword qudits for correcting the given erasures. The procedure has cubic complexity in the repair group size and the computed set of observables has the smallest possible size for correcting the given erasures. We specialize the general procedure to quantum codes constructed from Euclidean and Hermitian orthogonality, and provide closed-form upper bounds on the size of reduced repair groups for those special cases. Based on these closed-form bounds, we propose quantum counterparts of the information locality of classical local recovery.
Innovation
Methods, ideas, or system contributions that make the work stand out.
linear algebraic procedure
reduced set of observables
quantum information locality
cubic complexity
closed-form upper bounds
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