Phononic entanglement concentration via optomechanical interactions

Low-dissipation, tunable coupling to other quantum systems and unique features of phonons in the aspects of propagation, detection, and other areas suggest the applications of quantized mechanical oscillators in phonon-based quantum information processing (QIP) in a way different from their photonic counterpart. In this paper, we propose a 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 the future.