Overlap and entanglement-witness measurements

A feasible device for measurement of fidelity, overlap, purity, and Hilbert-Schmidt distance of two mixed states is proposed. In addition, this device realizes a decomposable entanglement witness-measurement for bipartite systems, corresponding to Werner criterion of entanglement. The measurement, based on interferometric setup and the control-phase gate, can be directly implemented in the cavity quantum electrodynamics, trapped ion, and electromagnetically induced transparency experiments.