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IEEE Vehicular Technology Conference

Entanglement Concentration for Concatenated Greenberger-Horne-Zeilinger State Assisted with Single Logic Qubit

Jun Pan, Rui Guo, Lan Zhou, Yu‐Bo Sheng

Published Jun 1, 2017• 0 citations
Publisher

Abstract

Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of logic-qubit entanglement, which has attracted a lot of attentions recently. We propose a protocol for concentrating the less-entangled C-GHZ state assisted with an auxiliary single logic qubit. In this protocol, by utilizing the quantum nondemolition detection (QND) constructed by cross-Kerr nonlinearities, we demonstrate that our protocol exhibits much higher success probability compared to conventional methods in linear optics. Moreover, the protocol requires less operations and classical communications. It may be useful in the implementation of long-distance quantum communication.

DOI
10.1109/vtcspring.2017.8108694

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Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new type of logic-qubit entanglement, which has attracted a lot of attentions recently. We propose a protocol for concentrating the less-entangled C-GHZ state assisted with an auxiliary single logic qubit. In this protocol, by utilizing the quantum nondemolition detection (QND) constructed by cross-Kerr nonlinearities, we demonstrate that our protocol exhibits much higher success probability compared to conventional methods in linear optics. Moreover, the protocol requires less operations and classical communications. It may be useful in the implementation of long-distance quantum communication.
Abstract The concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a new kind of logic-qubit entangled state, which may have extensive applications in future quantum communication. In this letter, we propose a protocol for constructing an arbitrary C-GHZ state with single photons. We exploit the cross-Kerr nonlinearity for this purpose. This protocol has some advantages over previous protocols. First, it only requires two kinds of cross-Kerr nonlinearities to generate single phase shifts ± θ . Second, it is not necessary to use sophisticated m -photon Toffoli gates. Third, this protocol is deterministic and can be used to generate an arbitrary C-GHZ state. This protocol may be useful in future quantum information processing based on the C-GHZ state.
Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.
The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state has great potential application in the future quantum network, for it is robust to the decoherence in a noisy environment. In the paper, we propose a complete C-GHZ state analysis protocol with the help of some auxiliary single atoms trapped in the low-quality cavities. In the protocol, we essentially make the parity check for the photonic states based on the photonic Faraday rotation effect, and complete the analysis task combined with the Hadamard operation and single qubit measurement. The success probability of our protocol can reach 100\% in principle, and the number of physical qubit encoded in each logic qubit does not affect the analysis. Our analysis protocol may have its practical application in future long-distance quantum communication.
The Bell state plays a significant role in the fundamental tests of quantum mechanics, such as the nonlocality of the quantum world. The Bell-state analysis is of vice importance in quantum communication. Existing Bell-state analysis protocols usually focus on the Bell-state encoding in the physical qubit directly. In this paper, we will describe an alternative approach to realize the near complete logic Bell-state analysis for the polarized concatenated Greenberger-Horne-Zeilinger (C-GHZ) state with two logic qubits. We show that the logic Bell-state can be distinguished in two steps with the help of the parity-check measurement (PCM) constructed by the cross-Kerr nonlinearity. This approach can be also used to distinguish arbitrary C-GHZ state with N logic qubits. As both the recent theoretical and experiment work showed that the C-GHZ state has its robust feature in practical noisy environment, this protocol may be useful in future long-distance quantum communication based on the logic-qubit entanglement.