We present the construction of standard entanglement-assisted (EA) qubit Reed-Muller (RM) codes and their tensor product variants from classical RM codes. We show that the EA RM codes obtained using the CSS construction have zero coding rate and negative catalytic rate. We further show that EA codes constructed from these same classical RM codes using the tensor product code (TPC) construction have positive coding rate and provide a subclass of EA RM TPCs that have positive catalytic rate, thus establishing the coding analog of superadditivity for this family of codes, useful towards quantum communications. We also generalize this analysis to obtain conditions for EA TPCs from classical codes to have positive catalytic rate when their corresponding EA CSS codes have zero rate.

中文翻译：

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纠缠辅助量子里德-米勒张量产品代码

我们提出了标准纠缠辅助 (EA) 量子位 Reed-Muller (RM) 代码的构造及其来自经典 RM 代码的张量积变体。我们表明，使用 CSS 构造获得的 EA RM 代码具有零编码率和负催化率。我们进一步表明，使用张量积代码（TPC）构造从这些相同的经典 RM 代码构建的 EA 代码具有正编码率，并提供具有正催化率的 EA RM TPC 子类，从而为该家族建立了超加性的编码类似物代码，对量子通信有用。我们还推广了这种分析，以获得当相应的 EA CSS 代码具有零速率时，经典代码中的 EA TPC 具有正催化速率的条件。