Phononic entanglement concentration via optomechanical interactions

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