The qubit reveals a qubit-cavity system

We show that the coupling between a qubit and a single mode cavity can be estimated from the process tomography data for the qubit alone. All the parameters of the coupling Hamiltonian between the qubit and the cavity mode can be obtained from observations on the qubit. We also show that the variance matrix and the photon number statistics of the single mode cavity can be reconstructed. Our results provide an alternate means of obtaining the coupling and reconstructing the state of the cavity mode in comparison with the techniques presently used.