  Motivated by the recent discovery of a quantum Chernoff theorem for
asymptotic state discrimination, we investigate the distinguishability of two
bipartite mixed states under the constraint of local operations and classical
communication (LOCC), in the limit of many copies. While for two pure states a
result of Walgate et al. shows that LOCC is just as powerful as global
measurements, data hiding states (DiVincenzo et al.) show that locality can
impose severe restrictions on the distinguishability of even orthogonal states.
Here we determine the optimal error probability and measurement to discriminate
many copies of particular data hiding states (extremal d x d Werner states) by
a linear programming approach. Surprisingly, the single-copy optimal
measurement remains optimal for n copies, in the sense that the best strategy
is measuring each copy separately, followed by a simple classical decision
rule. We also put a lower bound on the bias with which states can be
distinguished by separable operations.
