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Springer eBooks

Entanglement Purification

H. J. Briegel, B. Hüttner, N. Gisin, C. Macchiavello, M. Murao, Martin Bodo Plenio, Sandu Popescu, Vlatko Vedral, P. L. Knight, W. Dür, S. J. van Enk, J. I. Cirac, P. Zoller

Published Jan 1, 2000• 2 citations
Publisher
DOI
10.1007/978-3-662-04209-0_8

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Measurement-based entanglement purification for logical hybrid entanglement

Pei-Shun Yan, Xiao-Wei Mu, Zhang-Hua Cao

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.

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Principles of entanglement purification

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Observation of Residual Entanglement in Entanglement Purification

Lan Zhou, Cen-Xiao Huang, Yu‐Bo Sheng +6 more

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.

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A simplification of entanglement purification

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Measurement-based logical qubit entanglement purification

Peishun Yan, Lan Zhou, Wei Zhong +1 more

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.

Physical Review A•Jun 10, 2022•43 citations

Entanglement Purification via Entanglement Swapping

Scott Parker, Sougato Bose, Martin Bodo Plenio

Springer eBooks•Jan 1, 2003•1 citation
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.
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.