In quantum information theory, secret-key distillation is a crucial process for enabling secure communication across quantum networks. It works by extracting confidential bits from shared quantum states or channels using local operations and limited classical communication, ensuring privacy even over insecure links.

A bipartite quantum state is a system shared between two parties (often called Alice and Bob) that may exhibit entanglement. If they successfully distil a secret key, they can encrypt and decrypt messages securely, using the key like a shared password known only to them.

To achieve this, Alice and Bob use point-to-point quantum channels and perform local operations, meaning each can only manipulate their own part of the system. They also rely on one-way classical communication, where Alice sends messages to Bob, but Bob cannot reply. This constraint reflects realistic limitations in quantum networks and helps researchers identify the minimum requirements for secure key generation.

This paper investigates how many secret bits can be extracted under these conditions. The authors introduce a resource-theoretic framework based on unextendible entanglement which is a form of entanglement that cannot be shared with additional parties. This framework allows them to derive efficiently computable upper bounds on secret-key rates, helping determine how much security is achievable with limited resources.

Their results apply to both one-shot scenarios, where the quantum system is used only once, and asymptotic regimes, where the same system is used repeatedly and statistical patterns emerge. Notably, they extend their approach to quantum channels assisted by forward classical communication, resolving a long-standing open problem about the one-shot forward-assisted private capacity.

Finally, they show that error rates in private communication can decrease exponentially with repeated channel use, offering a scalable and practical path toward building secure quantum messaging systems.

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Distribution of entanglement in large-scale quantum networks by S Perseguers, G J Lapeyre Jr, D Cavalcanti, M Lewenstein and A Acín (2013)