Experimental measurement of multidimensional entanglement via equivalent symmetric projection

We construct a linear optics measurement process to determine the entanglement measure, named I concurrence, of a set of 4x4-dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an equivalent symmetric projection for the twofold copy of a single subsystem [presented by L. Aolita and F. Mintert, Phys. Rev. Lett. 97, 050501 (2006)] can be realized by observing the one-side two-photon coincidence without any triggering detection on the other subsystem. Here, for the first time, we realize the measurement for entanglement contained in biphoton pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the I concurrence of generic high-dimensional bipartite pure states produced in the parametric down conversion process.