We discuss how to generate entangled coherent states of four microwave resonators (a.k.a. cavities) coupled by a three-level superconducting device (qutrit). We also show that a Greenberger-Horne-Zeilinger (GHZ) state of four superconducting qubits embedded in four different resonators can be created with this scheme. In principle, the proposed method can be extended to create an entangled coherent state of
n resonators and to prepare a (GHZ) state of
n qubits distributed over
n cavities in a quantum network. In addition, it is noted that four resonators coupled by a coupler qutrit may be used as a basic circuit block to build a two-dimensional quantum network, which is useful for scalable quantum information processing.
We propose an efficient scheme for generating entangled states between a single nitrogen-vacancy (NV) centre in diamond and a superconducting qubit in a hybrid set-up. In this device, the NV centre and the superconducting qubit couple to a nanomechanical resonator and a superconducting coplanar waveguide cavity, respectively, while the microwave cavity and the mechanical resonator are parametrically coupled with a tunable coupling strength. We show that, highly entangled states between the NV centre and the superconducting qubit can be achieved, by means of the Jaynes–Cummings interactions in the NV-resonator and qubit-cavity subsystems which transfer the entanglement between the vibration phonons and the cavity photons to the NV centre and the superconducting qubit. This work may provide interesting applications in quantum computation and communication with single NV spins and superconducting qubits.
Provided that cavities are initially in a Greenberger-Horne-Zeilinger (GHZ) entangled state, we show that GHZ states of
N-group qubits distributed in
N cavities can be created via a three-step operation. The GHZ states of the
N-group qubits are generated by using
N-group qutrits placed in the
N cavities. Here, ``qutrit'' refers to a three-level quantum system with the two lowest levels representing a qubit while the third level acting as an intermediate state necessary for the GHZ state creation. This proposal does not depend on the architecture of the cavity-based quantum network and the way for coupling the cavities. The operation time is independent of the number of qubits. The GHZ states are prepared deterministically because no measurement on the states of qutrits or cavities is needed. In addition, the third energy level of the qutrits during the entire operation is virtually excited and thus decoherence from higher energy levels is greatly suppressed. This proposal is quite general and can in principle be applied to create GHZ states of many qubits using different types of physical qutrits (e.g., atoms, quantum dots, NV centers, various superconducting qutrits, etc.) distributed in multiple cavities. As a specific example, we further discuss the experimental feasibility of preparing a GHZ state of four-group transmon qubits (each group consisting of three qubits) distributed in four one-dimensional transmission line resonators arranged in an array.