Before revision:  To achieve this, we use Stein's method for Markov chains BN19, RR19 to show that a ``good'' coupling for a local Markov chain yields strong bounds on the spectral independence of the distribution in the sense of ALO20.
After revision:  To achieve this, we use Stein's method for Markov chains BN19, RR19 to show that a "good" coupling for a local Markov chain yields strong bounds on the spectral independence of the distribution in the sense of ALO20.