  In this paper we investigate the critical efficiency of detectors in order to
see Bell nonlocality using multiple copies of the two-qubit maximally entangled
state and local Pauli measurements which act in the corresponding qubit
subspaces. It is known that for the two-qubit maximally entangled state a
symmetric detection efficiency of $82.84\%$ can be tolerated using the
Clauser-Horne-Shimony-Holt (CHSH) Bell test. We show that this threshold can be
lowered by using multiple copies of the two-qubit maximally entangled state. We
get the upper bounds $80.86\%$, $73.99\%$ and $69.29\%$ on the symmetric
detection efficiency threshold for two, three and four copies of the state,
where the respective number of measurements per party are 4, 8 and 16. However,
in the case of four copies the result is partly due to a heuristic method. In
order to get the corresponding Bell inequalities we made use of linear
programming for two copies of the state and convex optimization based on
Gilbert algorithm for three and four copies of the state.
