  We provide rigorous, efficiently computable and tight bounds on the average
error probability of multiple-copy discrimination between qubit mixed states by
Local Operations assisted with Classical Communication (LOCC). In contrast to
the pure-state case, these experimentally feasible protocols perform strictly
worse than the general collective ones. Our numerical results indicate that the
gap between LOCC and collective error rates persists in the asymptotic limit.
In order for LOCC and collective protocols to achieve the same accuracy, the
former requires up to twice the number of copies of the latter. Our techniques
can be used to bound the power of LOCC strategies in other similar settings,
which is still one of the most elusive questions in quantum communication.
