CSS码上的概率分布：二泛性、QKD哈希、碰撞界、安全性
Probability distributions over CSS codes: two-universality, QKD hashing, collision bounds, security
AI总结：
本文通过引入新型等距映射，刻画CSS码上的概率分布，证明二泛QKD哈希协议的安全性依赖于随机矩阵的纯化态，并给出安全界。
摘要：
我们刻画了CSS码上的新型概率分布。这类纠错码最初由Calderbank、Shor和Steane提出，在推进量子计算保真度方面具有重要意义，并对近期应用有潜在影响。在量子密钥分发背景下，如Ostrev在arXiv:2109.06709中结合二泛哈希协议所研究的这类码，极大地简化了无条件安全量子计算阶段。为进一步研究二泛哈希协议的新应用，特别是通过奇偶校验矩阵的结构，我们展示了如何有效计算奇偶校验矩阵的函数与定义在随机矩阵上的适当概率测度的边缘分布之间的关系。二泛QKD哈希协议的安全性将依赖于随机矩阵纯化态的计算，这涉及两个哈希函数之间的概率碰撞界。我们方法的核心是引入新型实等距、模拟等距和理想等距，从而能够有效计算两个奇偶校验矩阵的函数。由于能够执行涉及奇偶校验矩阵的此类计算，二泛哈希协议的安全性降低了因子$2^{ \frac{5}{2} ( 5 - \frac{3}{2} ) + \mathrm{log}_2 \sqrt{C}}$，其中$C$为某个严格正常数。
英文摘要：
We characterize novel probability distributions for CSS codes. Such classes of error correcting codes, originally introduced by Calderbank, Shor, and Steane, are of great significance in advancing the fidelity of Quantum computation, with implications for future near term applications. Within the context of Quantum key distribution, such codes, as examined by Ostrev in arXiv: 2109.06709 along with two-universal hashing protocols, have greatly simplified Quantum phases of computation for unconditional security. To further examine novel applications of two-universal hashing protocols, particularly through the structure of parity check matrices, we demonstrate how being able to efficiently compute functions of the parity check matrices relates to marginals of a suitably defined probability measure supported over random matrices. The security of the two-universal QKD hashing protocol will be shown to depend upon the computation of purified states of random matrices, which relates to probabilistic collision bounds between two hashing functions. Central to our approach are the introduction of novel real, simulator, and ideal, isometries, hence allowing for efficient computations of functions of the two parity check matrices. As a result of being able to perform such computations involving parity check matrices, the security of the two-universal hashing protocol is a factor of $2^{ \frac{5}{2} ( 5 - \frac{3}{2} ) + \mathrm{log}_2 \sqrt{C}}$ less secure, for some strictly positive constant $C$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
