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Optics Express

Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime

Cong Cao, Chuan Xi Wang, Lingyan He, Ru Zhang

Published Feb 11, 2013• 81 citations
Publisher

Abstract

We investigate an atomic entanglement purification protocol based on the coherent state input-output process by working in low-Q cavity in the atom-cavity intermediate coupling region. The information of entangled states are encoded in three-level configured single atoms confined in separated one-side optical micro-cavities. Using the coherent state input-output process, we design a two-qubit parity check module (PCM), which allows the quantum nondemolition measurement for the atomic qubits, and show its use for remote parities to distill a high-fidelity atomic entangled ensemble from an initial mixed state ensemble nonlocally. The proposed scheme can further be used for unknown atomic states entanglement concentration. Also by exploiting the PCM, we describe a modified scheme for atomic entanglement concentration by introducing ancillary single atoms. As the coherent state input-output process is robust and scalable in realistic applications, and the detection in the PCM is based on the intensity of outgoing coherent state, the present protocols may be widely used in large-scaled and solid-based quantum repeater and quantum information processing.

DOI
10.1364/oe.21.004093

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We investigate an atomic entanglement purification protocol based on the coherent state input-output process by working in low-Q cavity in the atom-cavity intermediate coupling region. The information of entangled states are encoded in three-level configured single atoms confined in separated one-side optical micro-cavities. Using the coherent state input-output process, we design a two-qubit parity check module (PCM), which allows the quantum nondemolition measurement for the atomic qubits, and show its use for remote parities to distill a high-fidelity atomic entangled ensemble from an initial mixed state ensemble nonlocally. The proposed scheme can further be used for unknown atomic states entanglement concentration. Also by exploiting the PCM, we describe a modified scheme for atomic entanglement concentration by introducing ancillary single atoms. As the coherent state input-output process is robust and scalable in realistic applications, and the detection in the PCM is based on the intensity of outgoing coherent state, the present protocols may be widely used in large-scaled and solid-based quantum repeater and quantum information processing.
This paper presents an optimal entanglement concentration protocol (ECP) for entangled solid-state systems, using the coherent-state input–output process working in the low-Q cavity quantum electrodynamics regime. The solid-state system can be described as a three-level atom confined in a one-side optical microcavity. Using the ancillary coherent optical pulse to perform the cavity input–output process, different state-dependent phase shifts of the output coherent state can be discriminated by homodyne detection, and a less-entangled atomic pair can be concentrated to maximally entangled state in a certain probability between two remote parties nonlocally. By repeating the concentration process, the remote parties can further obtain a higher success probability. Compared with conventional ECPs, only one pair of less-entangled atoms is needed in the proposed protocol, and the coherent-state input–output process is working in a low-Q cavity in the atom–cavity intermediate coupling region. With feasible technologies, this protocol may be widely used in quantum repeaters and long-distance quantum communication.
Atomic ensembles are effective memory nodes for quantum communication network due to the long coherence time and the collective enhancement effect for the nonlinear interaction between an ensemble and a photon. Here we investigate the possibility of achieving the entanglement distillation for nonlocal atomic ensembles by the input-output process of a single photon as a result of cavity quantum electrodynamics. We give an optimal entanglement concentration protocol (ECP) for two-atomic-ensemble systems in a partially entangled pure state with known parameters and an efficient ECP for the systems in an unknown partially entangled pure state with a nondestructive parity-check detector (PCD). For the systems in a mixed entangled state, we introduce an entanglement purification protocol with PCDs. These entanglement distillation protocols have high fidelity and efficiency with current experimental techniques, and they are useful for quantum communication network with atomic-ensemble memories.
We propose a scheme to purify entanglement of two atoms from not-too-impure entangled states by checking the parity of the two atoms through the cavity input-output process. As the parity check is made by measurement on single-photon polarization, which would not affect the entanglement of the two atoms, our scheme has the successful probability double of that in a previous well-known scheme with linear optical elements [Nature (London) 410 (2001) 1067], and is insensitive to the photon loss and the detection inefficiency. Experimental feasibility of our scheme with current technology is discussed.
We present an atomic-state entangler with single atoms trapped in separated low-Q cavities, a coherent optical pulse as a quantum channel, a photon detector that only distinguishes the vacuum and nonvacuum states, and basic optical elements based on the input–output process in the intermediate coupling region with a higher probability and fidelity. The atomic-state entangler is meaningful because it does not need a strong coupling cavity and a single-photon source and could be feasible for large-scale quantum computation and quantum communication in the future. Based on this entangler, quantum information nonlocal transfer without classical communication, the quantum controlled-NOT gate, the four-particle |χ〉 state, the N-particle Greenberger-Horne-Zeilinger (GHZ) state, and cluster-state generation can be realized completely, which is useful in large-scale and nonlocal quantum information processing.
Solid quantum repeater is a core part in a large-scale quantum network. Entanglement purification, the key technique in a quantum repeater, is used to distill high-quality nonlocal entanglement from an ensemble in a mixed entangled state and to depress the vicious influence on quantum information carriers caused by noise. Here, we present an imperfect-interaction-free entanglement purification on nonlocal electron spins in quantum dots for solid quantum repeaters, using faithful parity check on electron spins. The faithful parity check can make correct judgement on the parity mode without destructing the nonlocal solid entanglement even with the imperfect interaction between a QD embedded inside a microcavity and a circularly polarized photon in the nearly realistic condition. Therefore, the imperfect-interaction-free entanglement purification can prevent the maximally entangled states from being changed into partially entangled ones and guarantee the fidelity of the nonlocal mixed state to a desired one after purification. As this scheme is feasible in the nearly realistic condition with imperfect interaction, the requirements for experimental implementation will be relaxed. These distinctive features make this imperfect-interaction-free entanglement purification have more practical applications in solid quantum repeaters for a large-scale quantum network.
In our previous paper [D. Gon\ifmmode \mbox{\c{t}}\else \c{t}\fi{}a and P. van Loock, Phys. Rev. A 84, 042303 (2011)], we proposed an efficient scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-not gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to control the entire scheme. Our improved distillation scheme yields an almost-unit output fidelity that, together with the entanglement distribution and swapping, opens an attractive route towards an efficient and experimentally feasible quantum repeater for long-distance quantum communication.