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

Abstract

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 $|\ddot{I}{ˆ}_N>={\sum }_{k=0}^{2^N-1}{\hat{I}}_k^2|k{>}_N$, 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 $|{\hat{I}}_k^2{|}^2$. 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.

5 pages, 3 figures