On general formulas for c-q channel resolvability, private capacity, and q-q capacity

Masafumi Hayashi

Ning Cai

Kabgyun Jeong

Graeme Smith

We study the symmetric-side-channel-assisted private capacity of a quantum channel, for which we provide a single- letter formula. This capacity is additive, convex, and, for degradable channels, equal to the unassisted private capacity. While a channel's (unassisted) capacity for private classical communication may be strictly larger than its quantum capacity, we will show that these capacities are equal for degradable channels, thus demonstrating the equivalence of privacy and quantum coherence in this context. We use these ideas to find new bounds on the key rate of quantum key distribution protocols with one-way classical post-processing. For the Bennett-Brassard-84 (BB84) protocol, our results demonstrate that collective attacks are strictly stronger than individual attacks.

Chengkai Zhu, Xin Wang

Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.

Kyongchun Lim, Changho Suh, June‐Koo Kevin Rhee