Joint quantum nondemolition measurements of qubits: beyond the mean-field theory

We propose an approach to nondestructively detect $N$ qubits by measuring the transmissions of a dispersively-coupled cavity. By taking into account all the cavity-qubits quantum correlations (i.e., beyond the usual coarse-grained/mean-field approximations), it is revealed that for an unknown normalized $N$-qubit state $|ψ_N>=\sum_{k=0}^{2^N-1}β_k|k>_N$, each detected peak in the cavity transmitted spectra marks one of the basis states $|k>_N$ and the relative height of such a peak is related to the corresponding superposed-probability $|β_k|^2$. Our results are able to unambiguously account for the intriguing multi-peak structures of the spectra observed in a very recent circuit-quantum-electrodynamics experiment [Phys. Rev. A {\bf 81}, 062325 (2010)] with two superconducting qubits.

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