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Optics Express

Imperfect-interaction-free entanglement purification on stationary systems for solid quantum repeaters

Guan-Yu Wang, Qing Ai, Fu‐Guo Deng, Bao‐Cang Ren

Published Jun 2, 2020• 10 citations
Publisher

Abstract

Solid quantum repeater is a core part in a large-scale quantum network. Entanglement purification, the key technique in a quantum repeater, is used to distill high-quality nonlocal entanglement from an ensemble in a mixed entangled state and to depress the vicious influence on quantum information carriers caused by noise. Here, we present an imperfect-interaction-free entanglement purification on nonlocal electron spins in quantum dots for solid quantum repeaters, using faithful parity check on electron spins. The faithful parity check can make correct judgement on the parity mode without destructing the nonlocal solid entanglement even with the imperfect interaction between a QD embedded inside a microcavity and a circularly polarized photon in the nearly realistic condition. Therefore, the imperfect-interaction-free entanglement purification can prevent the maximally entangled states from being changed into partially entangled ones and guarantee the fidelity of the nonlocal mixed state to a desired one after purification. As this scheme is feasible in the nearly realistic condition with imperfect interaction, the requirements for experimental implementation will be relaxed. These distinctive features make this imperfect-interaction-free entanglement purification have more practical applications in solid quantum repeaters for a large-scale quantum network.

DOI
10.1364/oe.394617

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Solid quantum repeater is a core part in a large-scale quantum network. Entanglement purification, the key technique in a quantum repeater, is used to distill high-quality nonlocal entanglement from an ensemble in a mixed entangled state and to depress the vicious influence on quantum information carriers caused by noise. Here, we present an imperfect-interaction-free entanglement purification on nonlocal electron spins in quantum dots for solid quantum repeaters, using faithful parity check on electron spins. The faithful parity check can make correct judgement on the parity mode without destructing the nonlocal solid entanglement even with the imperfect interaction between a QD embedded inside a microcavity and a circularly polarized photon in the nearly realistic condition. Therefore, the imperfect-interaction-free entanglement purification can prevent the maximally entangled states from being changed into partially entangled ones and guarantee the fidelity of the nonlocal mixed state to a desired one after purification. As this scheme is feasible in the nearly realistic condition with imperfect interaction, the requirements for experimental implementation will be relaxed. These distinctive features make this imperfect-interaction-free entanglement purification have more practical applications in solid quantum repeaters for a large-scale quantum network.
Recently, long distance of quantum communication relies on efficient quantum repeaters, and the distribution of maximal entanglement is a key technique for it. Especially, the distribution of entanglement with high-fidelity relies on the entanglement purification and concentration. Here we present a system to realize the entanglement purification for λ-type three-level entangled quantum dots by using the whispering-gallery-mode microcavity. Also we design a parity check gate on solid qubits that allows the quantum nondemolition measurement on the remote qubits. Moreover, one can distill a high-fidelity entangled solid state ensemble from a mixed-entangled state ensemble nonlocally.
High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11 km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332. The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as 6.6×10^{3} times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.
As the interaction between the photons and the environment which will make the entangled photon pairs in less entangled states or even in mixed states, the security and the efficiency of quantum communication will decrease. We present an efficient hyperentanglement purification protocol that distills nonlocal high-fidelity hyper-entangled Bell states in both polarization and spatial-mode degrees of freedom from ensembles of two-photon system in mixed states using linear optics. Here, we consider the influence of the photon loss in the channel which generally is ignored in the conventional entanglement purification and hyperentanglement purification (HEP) schemes. Compared with previous HEP schemes, our HEP scheme decreases the requirement for nonlocal resources by employing high-dimensional mode-check measurement, and leads to a higher fidelity, especially in the range where the conventional HEP schemes become invalid but our scheme still can work.
Abstract We use the quantum-dots (QD) coupled with single-sided microcavities system to construct the error-rejecting controlled not (CNOT) gate of electronic spins system in QD; We have designed an error-rejecting entanglement purification protocol (EPP) of electronic spins system in QD by using the error-rejecting CNOT gate and unitary operation. It can extract the high entanglement from the mixed entanglement states of the electronic spins with low entangled states. This EPP can eliminate the operation errors caused by the nonideal interaction between photons and QD coupled with optical microcavities system, and improve the fidelity of the EPP through iteration. Our scheme is more practical in future long-distance quantum communications, especially providing significant benefits for solving decoherence problems in quantum networks and quantum repeaters.
We propose a heralded quantum repeater protocol based on the general interface between the circularly polarized photon and the quantum dot embedded in a double-sided optical microcavity. Our effective time-bin encoding on photons results in the deterministic faithful entanglement distribution with one optical fiber for the transmission of each photon in our protocol, not two or more. Our efficient parity-check detector implemented with only one input-output process of a single photon as a result of cavity quantum electrodynamics makes the entanglement channel extension and entanglement purification in quantum repeater far more efficient than others, and it has the potential application in fault-tolerant quantum computation as well. Meanwhile, the deviation from a collective-noise channel leads to some phase-flip errors on the nonlocal electron spins shared by the parties and these errors can be depressed by our simplified entanglement purification process. Finally, we discuss the performance of our proposal, concluding that it is feasible with current technology.
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.