  Low dissipation, tunable coupling to other quantum systems, and unique
features of phonons in the aspects of propagation, detection and others suggest
the applications of quantized mechanical resonators in phonon-based quantum
information processing (QIP) in a way different from their photonic
counterpart. In this paper, we propose the first protocol of entanglement
concentration for nonlocal phonons from quantized mechanical vibration. We
combine the optomechanical cross-Kerr interaction with the Mach-Zehnder
interferometer and, by means of twice optomechanical interactions and the
photon analysis with respect to the output of the interferometer, achieve ideal
entanglement concentration about less-entangled nonlocal phonon Bell and
Greenberger-Horne-Zeilinger states. Our protocol is useful for preserving the
entangled phonons for the use of high quality phonon-based QIP in future.
