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Quantum Information Processing

Purification for hybrid logical qubit entanglement

Cheng‐Chen Luo, Lan Zhou, Wei Zhong, Yu‐Bo Sheng

Published Aug 20, 2022• 10 citations
Publisher
DOI
10.1007/s11128-022-03646-y

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Abstract Quantum entanglement is a fundamental resource for quantum computing, quantum communication, and quantum cryptography. In realistic quantum channels, however, entanglement is highly susceptible to noise and decoherence. Entanglement purification(EP) and quantum error correction (QEC) offer distinct approaches to protecting entanglement against noisy quantum channels. In this work, we propose a hybrid scheme that integrates these two approaches to enhance the protection of entanglement between logical qubits. The scheme exploits both the error-correcting capability of encoded logical qubits and the distillation power of entanglement purification, assuming recovery to the logical codespace after each QEC cycle. This combined approach enables improved entanglement preservation under noisy conditions. The resulting robust logical entanglement is well-suited for applications in quantum communication and quantum cryptography and offers a promising route toward more reliable distributed quantum information processing.
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 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.