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

TL;DR

This paper introduces a method for nondestructively measuring multiple qubits using cavity transmission spectra, accounting for quantum correlations beyond mean-field theory, and explains experimental multi-peak spectral structures.

Contribution

It develops a beyond mean-field theoretical framework for joint quantum nondemolition qubit measurements via cavity transmission, explaining complex spectral features.

Findings

Spectral peaks correspond to basis states of the qubits.

Peak heights relate to superposition probabilities.

The theory explains experimental multi-peak structures.

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 $|\psi_N>=\sum_{k=0}^{2^N-1}\beta_k|k>_N$, 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 $|\beta_k|^2$. 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.