No-go theorem for probabilistic one-way secret-key distillation

• URL: http://arxiv.org/abs/2404.01392v1
• Date: Mon, 1 Apr 2024 18:01:15 GMT
• Title: No-go theorem for probabilistic one-way secret-key distillation
• Authors: Vishal Singh, Mark M. Wilde,
• Abstract summary: Probability 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. We prove that an arbitrary state in this set cannot be used for probabilistic one-way secret-key distillation.
• Score: 4.079147243688764
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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