The heralded exact one-way distillable secret key is equal to the largest expected rate at which perfect secret key bits can be probabilistically distilled from a bipartite state by means of local operations and one-way classical communication. Here we define the set of super two-extendible states and prove that an arbitrary state in this set cannot be used for heralded exact one-way secret-key distillation. This broad class of states includes both erased states and all full-rank states. Comparing the heralded exact one-way distillable secret key with the more commonly studied approximate one-way distillable secret key, our results demonstrate an extreme gap between them for many states of interest, with the approximate one-way distillable secret key being much larger. Our findings naturally extend to heralded exact one-way entanglement distillation, with similar conclusions.

翻译：预示精确单向可提取秘密密钥等于通过局部操作和单向经典通信从二分态中概率性提取完美秘密密钥比特的最大期望速率。本文定义了超二可延拓态集合，并证明该集合中的任意态均不能用于预示精确单向秘密密钥提取。该广义态类既包含擦除态，也包含所有满秩态。通过比较预示精确单向可提取秘密密钥与更常研究的近似单向可提取秘密密钥，我们的结果表明对于许多重要态而言两者存在极端差距——近似单向可提取秘密密钥要大得多。我们的发现可自然推广至预示精确单向纠缠提取，并得到类似结论。