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arXiv:1511.02344 · Scientific Reports

Purification of Logic-Qubit Entanglement

Lan Zhou, Yu‐Bo Sheng

Published Jul 5, 2016• 73 citations
arXivHTMLPDF

Abstract

Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network.

DOI
10.1038/srep28813

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Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network.
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.
It has been found that logic-qubit entanglement has great potential for applications in quantum communication and quantum networks in recent years. However, along with the effects of noise and decoherence, the fidelity of the communication transmission can be greatly reduced. In this paper, we investigate the entanglement purification of logic bit-flip error and phase-flip error in polarization logic-qubit entanglement based on the parity-check measurement (PCM) gate, which is constructed by the cross-Kerr nonlinearity and used to distinguish the parity information of two-photon polarization states. The probability of entanglement purification is higher than the scheme using the linear optical method. Moreover, the quality of logic-qubit entangled states can be improved by a cyclic purification process. This entanglement purification protocol will be useful in the future when faced with long-distance communication with logic-qubit entanglement states.
Logic-qubit entanglement has attracted much attention in both quantum communication and quantum computation. Here, we present an efficient protocol to distill the logic-qubit entanglement with the help of cross-Kerr nonlinearity. This protocol not only can purify the logic bit-flip error and logic phase-flip error, but also can correct the physical bit-flip error completely. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors. Our distillation protocol for logic-qubit entanglement may be useful for the practical applications in quantum information, especially in long-distance quantum communication.
Measurement-based entanglement purification protocol (MBEPP) depending on the Bell state measurement (BSM) is first proposed in [Phys. Rev. Lett.110260503 (2013)10.1103/PhysRevLett.110.260503], which is shown to tolerate much more local noise than the conventional gate-based EPPs. However, the existing MBEPPs for discrete variable (MBEPP-DV) and MBEPP for continuous variable (MBEPP-CV) fail to take full advantage of their strengths. In this paper, we study the MBEPP for logical hybrid entanglement (MBEPP-LHE) in linear optics. We first demonstrate the principle of the MBEPP-LHE in the case that all logical BSMs (LBSMs) are perfect. Additionally, we consider that one of the components of the LBSM, i.e., the BSM for DVs or the BSM for CVs, fails on specific modes. The results indicate that the MBEPP-LHE can still work provided that at least one of the components of the LBSM is successful, which is the advantage of this purification compared to the previous MBEPPs. Moreover, the MBEPP-LHE can correct bit-flip and phase-flip errors not only on logical qubits but also on physical qubits. Furthermore, we show that the success probability of MBEPP-DV is the lower bound of that of MBEPP-LHE, while the success probability of the MBEPP-LHE has the same upper bound as MBEPP-CV. Finally, we also carry out the analysis of purifying the logical hybrid entanglement polluted by the dissipation error on coherent-state mode, and this error can be converted to bit-flip error on single-photon mode.
Recently Xiao et al. proposed a scheme for entanglement purification based on doubly entangled photon states (Phys. Rev. A 77(2008) 042315). We modify their scheme for improving the efficiency of entanglement purification. This modified scheme contains two steps, i.e., the bit-flip error correction and the entanglement purification of phase-flip errors. All the photon pairs in the first step can be kept as all the bit-flip errors are corrected. For purifying the phase-flip errors, a wavelength conversion process is needed. This scheme has the advantage of high efficiency and it requires the original fidelity of the entangled state wanted fay lower than other schemes, which makes it more feasible in a practical application.
Entanglement purification is the distilling of high-quality entanglement from low-quality entanglement and is a key element in the quantum repeater. As a new branch of entanglement purification, the measurement-based entanglement purification protocol (MBEPP) only requires one to perform the Bell state measurement to couple resource states with noisy pairs, and it tolerates more local noise than the conventional purification protocols. Existing MBEPPs usually focus on physical qubit entanglement. In this paper, we propose a measurement-based logical qubit entanglement purification protocol (MBLEPP) with quantum nondemolition detection (QND), where the qubit is encoded in the quantum parity code. The results show that this MBLEPP can also work with photon loss under the conditions that each block of the logical Bell state measurement contains at least one physical qubit, that at least one of the blocks is intact, and that the entanglement exists between all blocks. Moreover, we also consider the MBLEPP with imperfect QND. We show that below a certain QND error threshold, this MBLEPP can still work. In this way, this MBLEPP not only obtains high-fidelity entanglement but also tolerates photon loss and the error from imperfect QND. This MBLEPP combines the benefits of the MBEPP and quantum error correction code and may have potential application in long-distance quantum communication.