High-efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

Abstract

We propose a high-efficiency scheme to tomographically reconstruct an unknown quantum state by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the stationary transmissions through a driven dispersively coupled resonator. It is shown that only one kind of QND measurement is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining nondiagonal elements can be similarly determined by transferring them to the diagonal locations after a series of unitary operations. Compared with the tomographic reconstructions based on the usual destructive projective measurements (wherein one such measurement can determine only one diagonal element of the density matrix), the present reconstructive approach exhibits significantly high efficiency. Specifically, our generic proposal is demonstrated by the experimental circuit quantum electrodynamics systems with a few Josephson charge qubits. © 2011 American Physical Society.