论文标题
对称信息完整测量的化合物及其在量子密钥分布中的应用
Compounds of symmetric informationally complete measurements and their application in quantum key distribution
论文作者
论文摘要
在希尔伯特空间中，对称信息完整的测量（SIC）是优雅，著名且广泛有用的离散结构。我们介绍了一个更复杂的离散结构，该结构复杂化了几种SIC。 SIC-COMPOUND定义为$ D^3 $ vectors in $ d $二维的Hilbert Space的集合，可以通过两种不同的方式进行分区：成$ d $ sics，分成$ d^2 $正常基础。虽然当$ d> 2 $ $ d> 2 $时，他们的存在可能不太可能，但我们出人意料地通过$ d = 4 $的明确结构来回答它。值得注意的是，这种SIC混合物承认与互没有偏见的基础有着密切的关系，正如量子状态歧视所揭示的那样。除了基本的考虑之外，我们利用这些异国情调的特性来构建用于量子密钥分布的协议，并在一般的窃听攻击下分析其安全性。我们表明，在存在足够大的情况下，SIC-COMPOUND可以使安全的密钥生成能够防止六态协议的概括成功。
Symmetric informationally complete measurements (SICs) are elegant, celebrated and broadly useful discrete structures in Hilbert space. We introduce a more sophisticated discrete structure compounded by several SICs. A SIC-compound is defined to be a collection of $d^3$ vectors in $d$-dimensional Hilbert space that can be partitioned in two different ways: into $d$ SICs and into $d^2$ orthonormal bases. While a priori their existence may appear unlikely when $d>2$, we surprisingly answer it in the positive through an explicit construction for $d=4$. Remarkably this SIC-compound admits a close relation to mutually unbiased bases, as is revealed through quantum state discrimination. Going beyond fundamental considerations, we leverage these exotic properties to construct a protocol for quantum key distribution and analyze its security under general eavesdropping attacks. We show that SIC-compounds enable secure key generation in the presence of errors that are large enough to prevent the success of the generalisation of the six-state protocol.
