High efficiency tomographic reconstruction of quantum states by quantum nondemolition measurements

TL;DR

This paper introduces a highly efficient quantum state tomography method using quantum nondemolition measurements in circuit-QED systems, significantly reducing the number of measurements needed for reconstructing multi-qubit states.

Contribution

The paper presents a novel QND measurement-based scheme for quantum state tomography that improves efficiency over traditional destructive methods, applicable to multi-qubit systems.

Findings

QND measurements can determine all diagonal elements of the density matrix.

Spectral measurements combined with unitary operations can reconstruct off-diagonal elements.

Experimental demonstration in circuit-QED systems with Josephson charge qubits.

Abstract

We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the the stationary transmissions of the dispersively-coupled resonator. It is shown that only one kind of QND measurements is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining non-diagonal elements of the density matrix can be determined by other spectral measurements by beforehand transferring them to the diagonal locations using a series of unitary operations. Compared with the pervious tomographic reconstructions based on the usual destructively projective (DP) measurements (wherein one kind of such measurements could only determine one diagonal element of the density matrix), the present approach exhibits significantly high efficiency for N-qubit (N > 1). Specifically, our generic proposal is demonstrated by the experimental circuit-quantumelectrodynamics (circuit-QED) systems with a few Josephson charge qubits.