We study the symmetric-side-channel-assisted private capacity of a quantum channel, for which we providea single-letter formula. This capacity is additive, convex, and, for degradable channels, equal to the unassistedprivate capacity. While a channel's (unassisted) capacity for private classical communication may be strictlylarger than its quantum capacity, we will show that these capacities are equal for degradable channels, thusdemonstrating the equivalence of privacy and quantum coherence in this context. We use these ideas to findnew bounds on the key rate of quantum key distribution protocols with one-way classical post-processing. Forthe Bennett-Brassard 1984 protocol, our results demonstrate that collective attacks are strictly stronger thanindividual attacks.
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