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arXiv:1110.0059 · Physical Review A

Efficient multipartite entanglement purification with the entanglement link from a subspace

Fu‐Guo Deng

Published Nov 11, 2011• 115 citations
arXivHTMLPDF

Abstract

We present an efficient multipartite entanglement purification protocol (MEPP) for $N$-photon systems in a Greenberger-Horne-Zeilinger state with parity-check detectors. It contains two parts. One is the conventional MEPP with which the parties can obtain a high-fidelity $N$-photon ensemble directly, similar to the MEPP with controlled-not gates. The other is our recycling MEPP in which the entanglement link is used to produce some $N$-photon entangled systems from entangled ${N}^{\ensuremath{'}}$-photon subsystems ($2\ensuremath{\leqslant}{N}^{\ensuremath{'}}<N$) coming from the instances which are just discarded in all existing conventional MEPPs. The entangled ${N}^{\ensuremath{'}}$-photon subsystems are obtained efficiently by measuring the photons with potential bit-flip errors. With these two parts, the present MEPP has a higher efficiency than all other conventional MEPPs.

DOI
10.1103/physreva.84.052312

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We present an efficient multipartite entanglement purification protocol (MEPP) for NNN-photon systems in a Greenberger-Horne-Zeilinger state with parity-check detectors. It contains two parts. One is the conventional MEPP with which the parties can obtain a high-fidelity NNN-photon ensemble directly, similar to the MEPP with controlled-not gates. The other is our recycling MEPP in which the entanglement link is used to produce some NNN-photon entangled systems from entangled N\ensuremath′{N}^{\ensuremath{'}}N\ensuremath′-photon subsystems (2\ensuremath⩽N\ensuremath′<N2\ensuremath{\leqslant}{N}^{\ensuremath{'}}<N2\ensuremath⩽N\ensuremath′<N) coming from the instances which are just discarded in all existing conventional MEPPs. The entangled N\ensuremath′{N}^{\ensuremath{'}}N\ensuremath′-photon subsystems are obtained efficiently by measuring the photons with potential bit-flip errors. With these two parts, the present MEPP has a higher efficiency than all other conventional MEPPs.
We present an efficient and general multipartite entanglement purification protocol (MEPP) for N-photon systems in Greenberger-Horne-Zeilinger (GHZ) states with non-identical input states. As a branch of entanglement purification, besides the cases of successful purification, the recurrence MEPP actually has the reusable discarded items which are usually regarded as a failure. Our protocol contains two parts for bit-flip error correction. The first one is the conventional MEPP, corresponding successful cases. The second one includes two efficient approaches, recycling purification with entanglement link and direct residual entanglement purification, that can utilize discarded items. We also make a comparison between two approaches. Which method to use depends on initial input states, and in most cases the approach of direct residual purification is optimal for it not only may obtain a higher fidelity entangled state but also it does not require additional sophisticated links. In addition, for phase-flip errors, the discarded items still have available residual entanglement in the case of different input states. With these approaches, this MEPP has a higher efficiency than all previous MEPPs and it may have potential applications in the future long-distance quantum communications and networks.
Abstract Multipartite entanglement has been widely employed in quantum information processing. However, the unavoidable noise in quantum channels causes the maximally multipartite entangled state to degrade to the mixed state. In this paper, we propose a highly efficient multipartite entanglement purification protocol (MEPP) for the polarization Greenberger–Horne–Zeilinger state. Unlike conventional MEPPs, where two pairs of polluted entanglement are usually required, our protocol only requires one noisy copy of polarization-time-bin hyperentanglement and exploits the time-bin entanglement to purify the polarization entanglement. This feature increases the efficiency of our MEPP. Our MEPP may have potential applications in long-distance quantum communication.
We propose a multipartite entanglement purification protocol(MEPP) for photonic entangled states using low-Q cavities.In our MEPP,the multipartite photonic entangled states can be purified with the two steps,i.e.,bit-flip error correction and phase-flip error correction.We can repeat these two steps to get a hight-fidelity entangled photonic states.By the single photon input-output process regarding the low-Q cavity containing an atom,the parity of photonic polarization state can be nondestructive detect.Different from other photonic MEPPs,Our MEPP are nondestructive and feasible in current experiment conditions.
High-dimensional qudit (i.e., ddd-level or ddd-state) systems outperform two-dimensional qubit (i.e., 2-level or 2-state) systems in some quantum information processing tasks. We exploit entanglement purification protocols (EPPs) for extracting a subset of high quality arbitrary ddd-dimensional nnn-partite Greenberger-Horne-Zeilinger (GHZ) states from a large set of less entangled GHZ states. In our protocols, qudit-flip and phase-flip errors can be corrected, and the fidelity of the output state can be asymptotically improved to unity by iterating the EPP process. Moreover, the schemes are immune to the number of polluted photons, the fidelity thresholds of the proposed EPPs are developed, and the spatial-based single-qudit operations can be well manipulated with a range of balanced beam splitters, and phase shifters. These features make the proposed schemes offer an alternative method for high-dimensional multipartite entanglement purification.
We present a self-error-rejecting multipartite entanglement purification protocol (MEPP) for N-electron-spin entangled states, resorting to the single-side cavity-spin-coupling system. Our MEPP has a high efficiency containing two steps. One is to obtain high-fidelity N-electron-spin entangled systems with error-heralded parity-check devices (PCDs) in the same parity-mode outcome of three electron-spin pairs, as well as M-electron-spin entangled subsystems (2 ≤ M < N) in the different parity-mode outcomes of those. The other is to regain the N-electron-spin entangled systems from M-electron-spin entangled states utilizing entanglement link. Moreover, the quantum circuits of PCDs make our MEPP works faithfully, due to the practical photon-scattering deviations from the finite side leakage of the microcavity, and the limited coupling between a quantum dot and a cavity mode, converted into a failed detection in a heralded way.
A multiparticle entangled state is an indispensable resource in quantum information processing. However, the inherent noise in quantum channels may degrade the maximally entangled state to a mixed entangled state. An entanglement purification protocol (EPP) is a powerful tool to distill high-quality entanglement from low-quality entanglement. Conventional multiparticle EPPs (MEPPs) mainly focus on two noisy copies. In this paper, we investigate a single-copy MEPP (SCMEPP) in linear optics that requires only a pair of hyperentanglements. Specifically, we first purify the bit-flip errors for three-particle polarization Greenberger–Horne–Zeilinger (GHZ) states at the cost of time-bin entanglement, and then an analysis of correcting the phase-flip errors is carried out. Additionally, we extend this SCMEPP into purification for arbitrary multiparticle GHZ states. Moreover, we discuss the discarding components that have been regarded as failure in conventional two-copy MEPPs, and they still have entanglement if the fidelities of the initial states satisfy specific conditions. This can be reused to distill high-quality entanglement, therefore increasing the efficiency of the SCMEPP, which may have potential application to realize high-efficiency long-distance quantum communication.