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Physical Review A

Preparation of entangled states of four remote atomic qubits in decoherence-free subspace

Zhi Jiao Deng, Mang Feng, K. Gao

Published Feb 28, 2007• 92 citations
Publisher

Abstract

We propose how to prepare four remote logical qubits, with each in a separate cavity and encoded in the decoherence-free subspace by two atoms, into various entangled states. By means of the cavity-assisted photon scattering, we can link the four remote logical qubits in different cavities to be, respectively, $W$ state, Greenberger-Horne-Zeilinger state, and cluster state, which are important in view of the distributed quantum information processing. The generation of the latter two entangled states can be theoretically generalized to many-qubit cases. Because our qubits are defined in dephasing-free subspace, our scheme is immune to dephasing during or even after the entanglement preparation.

DOI
10.1103/physreva.75.024302

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We propose how to prepare four remote logical qubits, with each in a separate cavity and encoded in the decoherence-free subspace by two atoms, into various entangled states. By means of the cavity-assisted photon scattering, we can link the four remote logical qubits in different cavities to be, respectively, WWW state, Greenberger-Horne-Zeilinger state, and cluster state, which are important in view of the distributed quantum information processing. The generation of the latter two entangled states can be theoretically generalized to many-qubit cases. Because our qubits are defined in dephasing-free subspace, our scheme is immune to dephasing during or even after the entanglement preparation.
Based on the interference effect of polarized photons leaking out of separate cavities, we propose schemes for the generation of the N -atom Greenberger–Horne–Zeilinger (GHZ) state, three-atom W state and a genuine four-atom entangled state |χ⟩. In these schemes, each of the atoms is trapped separately in a remote optical cavity, and the possible spontaneous channels induced by the excited atoms lead to the coherent superposition of the states of the atoms. The desired multipartite entangled states can be generated with a certain success probability by the subsequent detection of the polarized photons in different modes. The schemes would be useful steps towards long-distance quantum communication, distributed quantum computation and constructing remote quantum information processing networks.
In general, implementing a multi-logical-qubit gate by manipulating quantum states in a decoherence-free subspace (DFS) becomes more complex and difficult when increasing the number of logical qubits. In this work, we propose an idea to realize quantum gates by manipulating quantum states outside their DFS but having the states of the logical qubits remain in their DFS before and after the gate operation. This proposal has the following features: (i) because the states are manipulated outside the DFS, the multiqubit gate implementation can be simplified when compared to realizing a multiqubit gate via manipulating quantum states within the DFS, which usually requires unitary operations over a large DFS, and (ii) because the states of the logical qubits return to the DFS after the gate operation, the errors caused by decoherence during the gate operation are not accumulated for a long-running calculation, and the states of the logical qubits are immune to decoherence when they are stored. Based on this proposal, we then present a way for realizing a multi-target-qubit controlled-not gate using logical qubits encoded in a decoherence-free subspace against collective dephasing. This gate is realized by employing qutrits (three-level quantum systems) placed in a cavity or coupled to a resonator. This proposal has the following advantages: (i) the states of the logical qubits return to their DFS after the gate operation; (ii) the gate can be implemented with only a few basic operations; (iii) the gate operation time is independent of the number of logical qubits; (iv) this gate can be deterministically implemented because no measurement is needed; (v) the intermediate higher-energy level for all qutrits is not occupied during the entire operation, thus decoherence from this level is greatly suppressed; (vi) this proposal is universal and can be applied to realize the proposed gate using natural atoms or artificial atoms (e.g., quantum dots, nitrogen-vacancy centers, and various superconducting qutrits, etc.) placed in a cavity or coupled to a resonator. As an application, we also show how to apply this gate to create a Greenberger-Horne-Zeilinger (GHZ) entangled state of multiple logical qubits encoded in DFS, and further investigate the experimental feasibility for creating the GHZ state of three logical qubits in the DFS, by using six superconducting transmon qutrits coupled to a one-dimensional coplanar waveguide resonator.
The existence of decoherence-free subspace (DFS) has been discussed widely. In this paper, we propose an alternative scheme for generating the four-atom W states by manipulating DF qubits. The atoms are divided into two pairs and trapped in two separate optical cavities. Manipulation of atoms within DFS may generate a two-atom maximally entangled state in an individual cavity, which is a stable state. After driving the system out of DFS, the atoms will interact resonantly with the cavity field. The photons leaking from the cavities interfere at the beamsplitter, which destroys which-path information, and are finally detected by one of the detectors, leading to the generation of a W state. In addition, the numerical simulation indicates that the fidelity of the prepared state can, for a very wide parameter regime, be very close to unity.
Important tasks in cavity quantum electrodynamics include the generation and control of quantum states of spatially separated particles distributed in different cavities. An interesting question in this context is how to prepare entanglement among particles located in different cavities, which are important for large-scale quantum information processing. We here consider a multi-cavity system where cavities are coupled to a superconducting (SC) qubit and each cavity hosts many SC qubits. We show that all intra-cavity SC qubits plus the coupler SC qubit can be prepared in an entangled Greenberger–Horne–Zeilinger (GHZ) state, by using a single operation and without the need of measurements. The GHZ state is created without exciting the cavity modes; thus greatly suppressing the decoherence caused by the cavity-photon decay and the effect of unwanted inter-cavity crosstalk on the operation. We also introduce two simple methods for entangling the intra-cavity SC qubits in a GHZ state. As an example, our numerical simulations show that it is feasible, with current circuit-QED technology, to prepare high-fidelity GHZ states, for up to nine SC qubits by using SC qubits distributed in two cavities. This proposal can in principle be used to implement a GHZ state for an arbitrary number of SC qubits distributed in multiple cavities. The proposal is quite general and can be applied to a wide range of physical systems, with the intra-cavity qubits being either atoms, NV centers, quantum dots, or various SC qubits.
We propose a unified scheme to generate WWW states, Greenberger-Horne-Zeilinger (GHZ) states, and cluster states of four distant atoms, which are trapped separately in leaky cavities. The proposed schemes require linear optical elements and photon detectors with single-photon sensitivity. The quantum noise influences the fidelity of the generated states. Further, based on the four-photon coincidence detection, we propose another scheme to generate the WWW states and GHZ states of four distant atoms. The scheme is insensitive to the quantum noise, but cannot be used to generate the cluster states.