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arXiv:quant-ph/0304069 · Physics Letters A

A simplification of entanglement purification

Jin-Yuan Hsieh, Che‐Ming Li, Der-San Chuu

Published Jun 17, 2004• 4 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2004.06.005

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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.
Entanglement purification is to distill high-quality entanglement from low-quality entanglement. Entanglement purification determines the efficiency and communication rates and plays a key role in quantum repeaters and long-distance quantum communications. Existing entanglement purification protocols and proof of principle experiments usually choose two identical input pairs. They are limited to focus on the successful purification case to obtain high-quality entangled states and discard the remained items if the purification fails. Recent entanglement purification theory [Opt. Express 28, 2291 (2020)OPEXFF1094-408710.1364/OE.383499] for arbitrary nonidentical input mixed states indicated that the discarded items may have residual entanglement and can be reused to increase the yield of entanglement purification, while the successful purification may not obtain a high-quality entangled state. In this Letter, using hyperentanglement, we design and experimentally demonstrate an entanglement purification protocol with nonidentical input mixed states. For the first time, we experimentally confirm the existence of residual entanglement in different error models. Furthermore, we illustrate that successful purification may decrease the fidelity of purified entangled states. We also demonstrate the approach of optimal entanglement purification. Our proof of principle results have potential applications in future high-efficiency and long-distance quantum communication.