Position-based coding and convex splitting for private communication over quantum channels

• Published in: Quantum information processing Vol. 16; no. 10; pp. 1 - 35
• Main Author: Wilde, Mark M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2017; Springer Nature B.V
• Subjects: Codes; Coding; Data Structures and Information Theory; Mathematical Physics; Physics; Physics and Astronomy; Quantum Computing; Quantum Information Technology; Quantum Physics; Spintronics; Splitting; Private classical communication; Second-order coding rate; Smooth max-mutual information; Quantum wiretap channel; Hypothesis testing mutual information
• ISSN: 1570-0755; 1573-1332
• DOI: 10.1007/s11128-017-1718-4

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 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 ε ∈ ( 0 , 1 ) . The present paper provides a lower bound on the 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.