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We propose a feasible approach to test Bell's inequality with theexperimentally-demonstrated circuit QED system, consisting of twowell-separated superconducting charge qubits (SCQs) dispersively coupled to acommon one-dimensional transmission line resonator (TLR). Our proposal is basedon the joint spectral measurements of the two SCQs, i.e., their quantum statesin the computational basis $\{|kl>,\,k,l=0,1\}$ can be measured by detectingthe transmission spectra of the driven TLR: each peak marks one of thecomputational basis and its relative height corresponds to the probabilitysuperposed. With these joint spectral measurements, the generated Bell statesof the two SCQs can be robustly confirmed without the standard tomographictechnique. Furthermore, the statistical nonlocal-correlations between these twodistant qubits can be directly read out by the joint spectral measurements, andconsequently the Bell's inequality can be tested by sequentially measuring therelevant correlations related to the suitably-selected sets of the classicallocal variables $\{\theta_j,\theta_j', j=1,2\}$. The experimental challenges ofour proposal are also analyzed.

Testing Bell inequalities with circuit QEDs by joint spectral measurements