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 $|{\phi}\rangle_{AB}$, every concentration rate below $S(\phi_A)$ is achievable by a single Schur--Weyl protocol depending only on the rate and local Hilbert spaces. For general sources along $\rho_{AB}$, every distillation rate below $E_D(\rho_{AB})$ 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 $E_D(\rho_{AB})$. For dilution, the entanglement cost of every MSR almost-iid target sequence along $\rho_{AB}$ is at most $E_F^\infty(\rho_{AB})$, the regularized entanglement of formation of the reference state. Consequently, every MSR almost-iid sequence along a pure reference state $|{\phi}\rangle_{AB}$ is asymptotically reversible, with distillable entanglement and entanglement cost equal to $S(\phi_A)$, 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.

Added universal entanglement distillation for MSR almost-iid sources with any prescribed $r_n=o(n)$, with uniform exponential error bounds. Extended asymptotic reversibility along pure reference states to include mixed MSR almost-iid sequences. Updated exposition and comparison with recent work. (38 pages)

arXiv:2606.06392 [quant-ph]

(or arXiv:2606.06392v2 [quant-ph] for this version)