Experimental Measurement of Multi-dimensional Entanglement via Equivalent Symmetric Projection

We construct a linear optics measurement process to determine the entanglement measure, named \emph{I-concurrence}, of a set of $4 \times 4$ dimensional two-photon entangled pure states produced in the optical parametric down conversion process. In our experiment, an \emph{equivalent} symmetric projection for the two-fold copy of single subsystem (presented by L. Aolita and F. Mintert, Phys. Rev. Lett. \textbf{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 bi-photon pure states by taking advantage of the indistinguishability and the bunching effect of photons. Our method can determine the \emph{I-concurrence} of generic high dimensional bipartite pure states produced in parametric down conversion process.