纠缠辅助量子局部恢复中可观测量与测量量子位的同时约简
Simultaneous Reduction of Observables and Measured Qudits in Entanglement-Assisted Quantum Local Recovery
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中文总结 AI 辅助
本文提出一种线性代数程序，同时约简纠缠辅助量子纠错码中的可观测量与修复组，以最小规模纠正擦除，并给出特殊码的闭式上界及量子信息局部性对应物。
中文摘要 AI 辅助
对于一般的纠缠辅助或非辅助量子纠错码、一组擦除以及相关联的修复组，我们提出了一种线性代数程序，用于计算约简的可观测量集合和码字量子位的约简修复组，以纠正给定的擦除。该程序在修复组规模上具有三次复杂度，并且计算出的可观测量集合对于纠正给定的擦除具有尽可能小的规模。我们将该通用程序专门应用于由欧几里得和厄米特正交性构造的量子码，并为这些特殊情况提供了约简修复组规模的闭式上界。基于这些闭式界，我们提出了经典局部恢复的信息局部性的量子对应物。
英文摘要
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.
发表机构
- Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。
