Direct measurement of two-qubit phononic entangled states via optomechanical interactions

We propose schemes of direct concurrence measurement for two-qubit phononic states from quantized mechanical vibration. By combining the Mach-Zehnder interferometer with the optomechanical cross-Kerr nonlinear effect, direct concurrence measurement schemes for two-qubit phononic entangled states are achieved with the help of photon detection with respect to the output of the interferometer. For different types of entangled states, diversified quantum devices and operations are designed accordingly. The final analysis shows reasonable performance under the current parameter conditions. Our schemes may be useful for potential phonon-based quantum computation and information in the future.