  Quantum entanglement is an indispensable resource for many significant
quantum information processing tasks. However, because of the noise in quantum
channels, it is difficult to distribute quantum entanglement over a long
distance in practice. A solution for this challenge is the quantum repeater
which can extend the distance of entanglement distribution. In this scheme, the
time consumption of classical communication and local operations takes an
important place in perspective of time efficiency. Motivated by this
observation, we exploit the basic quantum repeater scheme in perspectives of
not only the optimal rate of entanglement concentration but also the complexity
of local operations and classical communication. Firstly, we consider the case
where two two-qubit pure states are prepared. We construct a protocol with the
optimal entanglement concentration rate and less consumption of local
operations and classical communication. We also find a criteria for the
projective measurements to achieve the optimal probability. Secondly, we
exploit the case where two general pure states are prepared and general
measurements are considered. We get an upper bound on the probability for a
successful measurement operation to produce a maximally entangled state without
any further local operations.
