论文标题
Narain CFT的光谱与相关布尔函数的性质之间的关系
Relation between spectra of Narain CFTs and properties of associated boolean functions
论文作者
论文摘要
最近，已经发现了从某些类别的量子错误校正代码中构建Narain CFT。特别是，Narain CFT的光谱间隙对应于代码的二进制距离，而不是真正的锤击距离。在本文中，我们表明二进制距离与与量子代码独特相关的布尔函数的所谓EPC距离相同。因此，寻求具有较高光谱差距的Narain CFT等同于获得具有高EPC距离的布尔功能。此外，可以通过在布尔函数的二进制真实表方面找到较低的峰值功率比（PAR）来解决此问题。尽管对于高EPC距离来说，这既不足够也不是必要的条件，但我们构建了一些相对较高的EPC距离的示例，这些示例是指较低PAR的结构。我们还看到，具有高距离的代码与独立数较低的诱导图有关。
Recently, the construction of Narain CFT from a certain class of quantum error correcting codes has been discovered. In particular, the spectral gap of Narain CFT corresponds to the binary distance of the code, not the genuine Hamming distance. In this paper, we show that the binary distance is identical to the so-called EPC distance of the boolean function uniquely associated with the quantum code. Therefore, seeking Narain CFT with high spectral gap is equivalent to getting a boolean function with high EPC distance. Furthermore, this problem can be addressed by finding lower Peak-to-Average Power ratio (PAR) with respect to the binary truth table of the boolean function. Though this is neither sufficient nor necessary condition for high EPC distance, we construct some examples of relatively high EPC distances referring to the constructions for lower PAR. We also see that codes with high distance are related to induced graphs with low independence numbers.
