Robustness of Entanglement Manipulation for almost i.i.d. sources

Abstract

We study the robustness of asymptotic entanglement manipulation for Mazzola--Sutter--Renner (MSR) almost-iid sources, which allow a sublinear number of deviations from tensor-power structure. For pure sources along $|φ\rangle_{AB}$, every concentration rate below $S(φ_A)$ is achievable by a single Schur--Weyl protocol depending only on the rate and local Hilbert spaces. For general sources along $ρ_{AB}$, every distillation rate below $E_D(ρ_{AB})$ is achievable by a single LOCC protocol sequence independent of the particular source and defect size. Its error vanishes exponentially and uniformly for each prescribed defect bound $r_n=o(n)$, yielding an optimal universal distillation rate equal to $E_D(ρ_{AB})$. For dilution, the entanglement cost of every MSR almost-iid target sequence along $ρ_{AB}$ is at most $E_F^\infty(ρ_{AB})$, the regularized entanglement of formation of the reference state. Consequently, every MSR almost-iid sequence along a pure reference state $|φ\rangle_{AB}$ is asymptotically reversible, with distillable entanglement and entanglement cost equal to $S(φ_A)$, even when its individual states are mixed. The proofs establish structural and entropic properties of MSR almost-iid sources that may be useful in other information-theoretic settings.