Permutationally invariant tomography of a four-qubit symmetric Dicke state

Here, the authors present experimental results of the tomographic analysis of a photonic four-qubit symmetric Dicke state. Instead of 34=81 basis settings for full tomography only 15 basis settings have to be measured for permutationally invariant tomography. A further advantage of our method is that the single qubits do not have to be individually manipulable since for each measurement the same local setting is applied to all qubits. The best performance of our measurement algorithm is achieved when the basis settings are evenly distributed on the Bloch sphere. In our experiments we showed that the overlap between the density matrix obtained from full tomography and the one obtained from permutationally invariant tomography, and thus the permutationally invariant component of the observed quantum state was 94.7%.