Two-qubit tomography with joint dispersive read-out in circuit QED

Quantum state tomography is an important tool in quantum information science for complete characterization of multi-qubit states and their correlations. We demonstrate that for two superconducting qubits coupled to a common resonator mode a reconstruction of the full density matrix can be achieved by measuring the transmission through the resonator -- without the need for single-shot measurement of individual qubits. Since the resonator transmission depends non-linearly on the dispersive cavity pull of different qubit states, information about qubit-qubit correlations is intrinsically present in the averaged measurement signal. It is shown that this simultaneous two-qubit read-out can be used for quantum state tomography of both separable and entangled states.