Second-Order Converse for Rate-Limited Common Randomness Generation

We employ a recent technique based on a semigroup application of the method of types to improve on a second-order converse for the common randomness (CR) generation problem. The previously known bound lead to a correct second-order asymptotic rate, but incorrect sign on the second-order term for error rates below 1/2. The new bound has both the correct scaling and sign of the second-order term for small enough error rates.