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Physical Review A

Complete logic Bell-state analysis assisted with photonic Faraday rotation

Lan Zhou, Yu‐Bo Sheng

Published Oct 12, 2015• 101 citations
Publisher

Abstract

The logic Bell-state which encodes many physical qubits in a logic qubit has great application potential in the future quantum communication field, for it is robust to the decoherence in a noisy environment. In this paper, we propose a complete logic Bell-state analysis (LBSA) with the help of the auxiliary single atoms trapped in the low-quality cavity. We construct the parity-check measurement gate based on the photonic Faraday rotation effect and complete the task combined with the Hadamard operation and single-qubit measurement. The number of physical qubits encoded in each logic qubit does not affect the analysis. We also discuss the application of this LBSA in the fields of quantum teleportation and logic-qubit entanglement swapping. Our LBSA protocol may have practical application in future long-distance quantum communication.

DOI
10.1103/physreva.92.042314

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The logic Bell-state which encodes many physical qubits in a logic qubit has great application potential in the future quantum communication field, for it is robust to the decoherence in a noisy environment. In this paper, we propose a complete logic Bell-state analysis (LBSA) with the help of the auxiliary single atoms trapped in the low-quality cavity. We construct the parity-check measurement gate based on the photonic Faraday rotation effect and complete the task combined with the Hadamard operation and single-qubit measurement. The number of physical qubits encoded in each logic qubit does not affect the analysis. We also discuss the application of this LBSA in the fields of quantum teleportation and logic-qubit entanglement swapping. Our LBSA protocol may have practical application 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.
Decoherence is one of the main obstacles in long-distance quantum communication. Recently, the theoretical work of Fröwis and W. Dür (Phys. Rev. Lett. \textbf{106}, 110402 (2011)) and the experiment of Lu \emph{et al.} (Nat. Photon. \textbf{8}, 364 (2014)) both showed that the logic qubits entanglement say the concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is more robust under decoherence. In this paper, we describe a protocol for Bell-state analysis for this logic qubits entanglement. This protocol can also be extended to the multipartite C-GHZ state analysis. Also, we discuss its application in the quantum teleportation of a unknown logic qubit and in the entanglement swapping of logic Bell states. As the logic qubits entanglement is more robust under decoherence, our protocol shows that it is possible to realize the long-distance quantum communication based on logic qubits entanglement.
Logic-qubit entanglement is a promising resource in quantum information processing, especially in future large-scale quantum networks. In the paper, we put forward an efficient entanglement purification protocol (EPP) for nonlocal mixed logic entangled states with the bit-flip error in the logic qubits of the logic Bell state, resorting to the photon-atom interaction in low-quality (Q) cavity and atomic state measurement. Different from existing EPPs, this protocol can also purify the logic phase-flip error, and the bit-flip error and the phase-flip error in physic qubit. During the protocol, we only require to measure the atom states, and it is useful for improving the entanglement of photon systems in future large-scale quantum networks.
We propose an efficient protocol for measuring the concurrence of arbitrary two-photon pure entangled state with the help of the photonic Faraday rotation. In the protocol, the concurrence of the photonic entangled state can be conversed into the total success probability for picking up the odd-parity photonic state. For completing the measurement task, we require some auxiliary three-level atoms, which are trapped in the low-quality cavities. Our protocol can be well realized under current experimental conditions. Moreover, under practical imperfect atom state detection and photonic Faraday rotation conditions, our protocol can also work well. Based on these features, our protocol may be useful in current quantum information processing.
Logical entangled states are essential for quantum information processing due to their robustness against environmental noise and decoherence. We propose a scheme for generating logical cluster states based on photonic Faraday rotation in atom-cavity coupling systems. A physical cluster state is generated first. Subsequently, additional single photons assist in transforming each physical qubit into a physical GHZ state, which serves as a logical qubit. After replacing all physical qubits with logical qubits, the logical cluster state is obtained. The responses of photon detectors reveal low-probability errors arising from photon input-output imbalances, but these measurements do not induce scheme failure. Optical attenuators balance optical paths, guaranteeing unity fidelity in theory.