Permutationally invariant tomography of a four-qubit symmetric Dicke state

Multi-partite entangled quantum states play an important role in quantum information processing with applications, for example, in quantum enhanced metrology or quantum communication. Therefore, efficient measurement schemes to fully characterize these states are needed. However, conventional quantum state tomography which reveals all properties of a quantum state suffers from an exponentially increasing measurement effort with the number of qubits.