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Vishal Singh, Mark M. Wilde (Apr 03 2024).

Abstract: The probabilistic 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 probabilistic one-way secret-key distillation. This broad class of states includes both erased states and all full-rank states. Comparing the probabilistic 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 probabilistic one-way entanglement distillation, with similar conclusions.

Arxiv: https://arxiv.org/abs/2404.01392