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The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit-cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. This scheme becomes problematic in the case of strong coupling and/or strong measurement drive, owing to the so-called Purcell effect. A recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity, and {it ideal QND} readout of qubit state. The aim of the present work is twofold: (i) In parallel to what has been done in the past years for the dispersive readout, we carry out the gradual partial-collapse theory for this recent scheme, in terms of both the quantum trajectory equation and quantum Bayesian approaches. The partial-collapse weak measurement theory is useful for such as the measurement-based feedback control and other quantum applications. (ii) In the physical aspect, we construct the joint qubit-plus-cavity entangled state under continuous measurement and present a comprehensive analysis for the quantum efficiency,qubit-state purity, and signal-to-noise ratio in the output currents. The combination of the joint state and the quantum Bayesian rule provides a generalized scheme of cavity reset associated with the longitudinal coupling, which can restore the qubit to a quantum pure state from entanglement with the cavity states, and thus benefits the successive partial-collapse measurements after qubit rotations.
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 approxim
Developing efficient framework for quantum measurements is of essential importance to quantum science and technology. In this work, for the important superconducting circuit-QED setup, we present a rigorous and analytic solution for the effective qua
We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto n coherent-state (CS) qubits, by employing 2n microwave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS
Photonic states of superconducting microwave cavities controlled by transmon ancillas provide a platform for encoding and manipulating quantum information. A key challenge in scaling up the platform is the requirement to communicate on demand the inf
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits (cqubits) via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit.