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Europhysics Letters (EPL)

Entanglement analysis for macroscopic Schrödinger's Cat state

Yu‐Bo Sheng, Lan Zhou

Published Feb 1, 2015• 25 citations
Publisher

Abstract

Macroscopic entanglement, or say the Schrödinger's Cat state has attracted much attention for a long time. Recently, the first theoretical work of Fröwis and Dür ( Phys. Rev. Lett. , 106 (2011) 110402) and the first experiment of Lu et al. ( Nat. Photon. , 8 (2014) 364) both showed that, a new type of Schrödinger's Cat state, the logic-qubit entanglement (concatenated Greenberger-Horne-Zeilinger (C-GHZ) state) is immune and robust to the noise, and is possible to be applied in future large-scale quantum networks. In this paper, we describe a protocol of entanglement analysis for this kind of Schrödinger's Cat state. Both the Bell-state type of logic-qubit entanglement and multipartite C-GHZ state can be completely distinguished. Based on the entanglement analysis, an arbitrary unknown macroscopic Schrödinger's Cat superposed state can be teleportated and we can also perform the macroscopic entanglement swapping. Our protocol shows that it is possible to realize long-distance quantum communication and large-scale quantum network based on logic-qubit entanglement.

DOI
10.1209/0295-5075/109/40009

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Macroscopic entanglement, or say the Schrödinger's Cat state has attracted much attention for a long time. Recently, the first theoretical work of Fröwis and Dür ( Phys. Rev. Lett. , 106 (2011) 110402) and the first experiment of Lu et al. ( Nat. Photon. , 8 (2014) 364) both showed that, a new type of Schrödinger's Cat state, the logic-qubit entanglement (concatenated Greenberger-Horne-Zeilinger (C-GHZ) state) is immune and robust to the noise, and is possible to be applied in future large-scale quantum networks. In this paper, we describe a protocol of entanglement analysis for this kind of Schrödinger's Cat state. Both the Bell-state type of logic-qubit entanglement and multipartite C-GHZ state can be completely distinguished. Based on the entanglement analysis, an arbitrary unknown macroscopic Schrödinger's Cat superposed state can be teleportated and we can also perform the macroscopic entanglement swapping. Our protocol shows that it is possible to realize long-distance quantum communication and large-scale quantum network based on 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.
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.
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.
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.
Entanglement is the quintessential quantum phenomenon and a key enabler of quantum algorithms. The ability to faithfully entangle many distinct particles is often used as a benchmark for the quality of hardware and control in a quantum computer. Greenberger-Horne-Zeilinger (GHZ) states, also known as Schrödinger cat states, are useful for this task. They are easy to verify, but difficult to prepare due to their high sensitivity to noise. In this Letter we report on the largest GHZ state prepared to date consisting of 120 superconducting qubits. We do this via a combination of optimized compilation, low-overhead error detection and temporary uncomputation. We use an automated compiler to maximize error-detection in state preparation circuits subject to arbitrary qubit connectivity constraints and variations in error rates. We measure a GHZ fidelity of 0.56(3) with a post-selection rate of 28%. We certify the fidelity of our GHZ states using multiple methods and show that they are all equivalent, albeit with different practical considerations.