Convergence rate of the Werner-state linear-program hierarchy

Determine a quantitative convergence rate for the normalized finite-copy linear-program lower bounds $L(\rho_p^{\otimes m})/m$ to the PPT distillable entanglement of Werner states.

Background

For Werner states, the regularised characterization reduces each finite-copy level to an exact finite linear program. The normalized levels form running lower bounds converging to the operational PPT distillable entanglement, but the paper does not provide a bound on how quickly this convergence occurs. Establishing such a rate would quantify the number of copies needed to approximate the asymptotic distillation rate.