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

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.

Single-photon-added coherent state based measurement transition and its advantages in precision measurement

“…This strong quantum measurement model promotes the exploring of the quantum theory from its fundamentals [2][3][4][5][6][7] to quantum art technologies [8][9][10][11][12][13][14][15]. However, because of the collapse of wave function owing to the decoherence, the conventional strong quantum measurements cannot be directly used in some hot topics of quantum information science such as quantum sate based high precision measurements [16][17][18][19], reconstruction of unknown quantum state [20][21][22][23], etc. On the other hand, this strong measurement model becomes useless if the coupling between measured system and pointer is too weak to distinguish the different eigenvalues of the observable.…”