2024/10/28 by Aadil Oufkir, Mario Berta, Oufkir, Aadil +1 · 1 citation
Computer Science · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography
paper · pdf · doi:10.48550/arxiv.2410.21124
We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation -- termed meta-converse -- are equivalent in terms of success probabilities. We then present a rounding procedure that transforms any non-signaling-assisted strategy into an entanglement-assisted one and prove an approximation ratio of (1 - e-1) in success probabilities for the special case of measurement channels. For fully quantum channels, we give a weaker (dimension dependent) approximation ratio, that is nevertheless still tight to characterize the strong converse exponent of entanglement-assisted channel coding [Li and Yao, IEEE Tran.~Inf.~Theory (2024)]. Our derivations leverage ideas from position-based coding, quantum decoupling theorems, the matrix Chernoff inequality, and input flattening techniques.