LAUSR

The classical-input quantum-output (cq) wiretap channel is a communication model involving a classical sender X, a legitimate quantum receiver B, and a quantum eavesdropper E. The goal of a private communication protocol that uses such a channel is for the sender X to transmit a message in such a way that the legitimate receiver B can decode it reliably, while the eavesdropper E learns essentially nothing about which message was transmitted. The $$\varepsilon $$ε-one-shot private capacity of a cq wiretap channel is equal to the maximum number of bits that can be transmitted over the channel, such that the privacy error is no larger than $$\varepsilon \in (0,1)$$ε∈(0,1). The present paper provides a lower bound on the $$\varepsilon $$ε-one-shot private classical capacity, by exploiting the recently developed techniques of Anshu, Devabathini, Jain, and Warsi, called position-based coding and convex splitting. The lower bound is equal to a difference of the hypothesis testing mutual information between X and B and the “alternate” smooth max-information between X and E. The one-shot lower bound then leads to a non-trivial lower bound on the second-order coding rate for private classical communication over a memoryless cq wiretap channel.