Narain CFTs谱与相关布尔函数性质的关系
Relation between spectra of Narain CFTs and properties of associated boolean functions
摘要：
最近，从一类量子纠错码中构造出了Narain CFT。特别地，Narain CFT的频谱间隙对应于代码的二进制距离，而不是真正的汉明距离。在本文中，我们表明，二进制距离是相同的所谓的EPC距离的布尔函数唯一关联的量子代码。因此，寻找具有高光谱间隙的Narain CFT相当于获得具有高EPC距离的布尔函数。此外，该问题可以通过相对于布尔函数的二进制真值表找到较低的峰值与平均功率比（PAR）来解决。虽然这不是高EPC距离的充分条件也不是必要条件，但我们构造了一些相对高EPC距离的例子，参考了较低PAR的构造。我们还看到，具有高距离的代码与具有低独立数的诱导图有关。
英文摘要：
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.
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