Rate 1/5 Non-Malleable Codes against Entangled Split-State Tampering

We construct efficient information-theoretic non-malleable codes for classical messages that are secure against two noncommunicating local quantum tampering operations with arbitrary pre-shared entanglement. For every sufficiently small fixed $\xi >0$ and all sufficiently large first-share lengths $n$, the codes have rate at least $1\mathrm{/}5-\xi$, perfect correctness, and error $2^{-n^{\mathrm{\Omega }(1)}}$. Security holds for every message, with a single message-independent simulator for each attack. This resolves the constant-rate question for worst-case classical messages in the entangled two-split-state model. Our construction builds on the permutation-based two-split construction of Batra, Boddu, and Jain, which achieves rate approaching $1\mathrm{/}5$ for uniformly random messages. We retain their architecture but replace the uniform message input to the permutation with a prescribed message concatenated with fresh uniform padding. Our main contribution is a worst-case security reduction for this modification.