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arXiv:0705.3991 · Physical Review B

Macroscopic Greenberger-Horne-Zeilinger and W states in flux qubits

Mun Dae Kim, Sam Young Cho

Published Mar 26, 2008• 26 citations
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Abstract

We investigate two types of genuine three-qubit entanglement, known as the Greenberger-Horne-Zeilinger (GHZ) and $W$ states, in a macroscopic quantum system. Superconducting flux qubits are theoretically considered in order to generate such states. A phase coupling is proposed to offer enough strength of interactions between qubits. While an excited state can be the $W$ state, the GHZ state is formed at the ground state of the three flux qubits. The GHZ and $W$ states are shown to be robust against external flux fluctuations for feasible experimental realizations.

DOI
10.1103/physrevb.77.100508

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We investigate two types of genuine three-qubit entanglement, known as the Greenberger-Horne-Zeilinger (GHZ) and WWW states, in a macroscopic quantum system. Superconducting flux qubits are theoretically considered in order to generate such states. A phase coupling is proposed to offer enough strength of interactions between qubits. While an excited state can be the WWW state, the GHZ state is formed at the ground state of the three flux qubits. The GHZ and WWW states are shown to be robust against external flux fluctuations for feasible experimental realizations.
We theoretically study the macroscopic quantum entanglement in superconducting flux qubits. A phase-coupling scheme is proposed to offer enough strength of interactions between qubits. It is shown that due to the two-qubit tunneling processes both the ground state and excited states of coupled two flux qubits can be Bell type states, maximally entangled, in experimentally accessible regimes. The parameter regimes for the Bell states are discussed in terms of external magnetic flux and Josephson coupling energies. We also investigate two types of genuine three-qubit entanglement, known as the Greenberger-Horne- Zeilinger(GHZ) and W states. While an excited state can be the W state, the GHZ state is formed at the ground state of the coupled three flux qubits. The GHZ and W states are shown to be robust against external flux fluctuations for feasible experimental realizations.
We propose a scheme to generate Greenberger-Horne-Zeilinger (GHZ) state for N superconducting qubits in a circuit QED system. By sinusoidally modulating the qubit-qubit coupling, a synthetic magnetic field has been made which broken the time-reversal symmetry of the system. Directional rotation of qubit excitation can be realized in a three-qubit loop under the artificial magnetic field. Based on the special quality that the rotation of qubit excitation has different direction for single- and double-excitation loops, we can generate three-qubit GHZ state and extend this preparation method to arbitrary multiqubit GHZ state. Our analysis also shows that the scheme is robust to various operation errors and environmental noise.
Going beyond the entanglement of microscopic objects (such as photons, spins, and ions), here we propose an efficient approach to produce and control the quantum entanglement of three macroscopic coupled superconducting qubits. By conditionally rotating, one by one, selected Josephson-charge qubits, we show that their Greenberger-Horne-Zeilinger (GHZ) entangled states can be deterministically generated. The existence of GHZ correlations between these qubits could be experimentally demonstrated by effective single-qubit operations followed by high-fidelity single-shot readouts. The possibility of using the prepared GHZ correlations to test the macroscopic conflict between the noncommutativity of quantum mechanics and the commutativity of classical physics is also discussed.
We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically, because no measurement is involved. Numerical simulations show that the high-fidelity generation of a three-cqubit GHZ state is feasible with the present circuit QED technology. This proposal can be easily extended to create a N-cqubit GHZ state (N≥3), with N microwave or optical cavities coupled to a natural or artificial three-level atom.
Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the WWW state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal NNN-qubit GHZ state to a state arbitrarily close to the ideal NNN-qubit WWW state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.