Linear Optical Implemention of a Quantum Network for Quantum Estimation

We present a scheme for simulating the quantum network of quantum estimation proposed by A. K. Ekert et al. [Phys. Rev. Lett. 88, 217901 (2002)]. We experimentally implement the scheme with linear optical elements. We perform overlap measurements of two single-qubit states and entanglement-witness measurements of some two-qubit states. In addition, it can also be used for entanglement quantification for some kinds of states. From the other perspective, we physically realize the positive but not completely positive map, transposition.