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Optics Express

Feasible measurement-based entanglement purification in linear optics

Peishun Yan, Lan Zhou, Wei Zhong, Yu‐Bo Sheng

Published Mar 2, 2021• 34 citations
Publisher

Abstract

Entanglement purification is used to distill high quality entangled states from several noisy low quality entangled states, and it plays a key role in quantum repeater. The measurement-based entanglement purification protocol (MB-EPP) does not require local two-qubit gates or single-particle measurements on the noisy pairs and may offer significant advantages compared with the gate-based EPPs. We present an alternative MB-EPP in linear optics. Subsequently, we provide a detailed analysis on the realization of this MB-EPP using spontaneous parametric down conversion (SPDC) sources. By delicately designing the optical circuits, the double-pair emission noise caused by SPDC sources can be eliminated automatically. Combined with suitable quantum memory and entanglement swapping, this MB-EPP may have application potential in the implementation of a practical measurement-based quantum repeater.

DOI
10.1364/oe.420348

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Entanglement purification is used to distill high quality entangled states from several noisy low quality entangled states, and it plays a key role in quantum repeater. The measurement-based entanglement purification protocol (MB-EPP) does not require local two-qubit gates or single-particle measurements on the noisy pairs and may offer significant advantages compared with the gate-based EPPs. We present an alternative MB-EPP in linear optics. Subsequently, we provide a detailed analysis on the realization of this MB-EPP using spontaneous parametric down conversion (SPDC) sources. By delicately designing the optical circuits, the double-pair emission noise caused by SPDC sources can be eliminated automatically. Combined with suitable quantum memory and entanglement swapping, this MB-EPP may have application potential in the implementation of a practical measurement-based quantum repeater.
High quality time-bin entanglement is widely exploited to achieve the purposes of fundamental tests of physics and the implementation of quantum communication protocols both in free space and optical fiber propagation. However, the imperfect approaches of generating time-bin entangled state will degrade its quality and limit its practical application. Entanglement purification is to distill high quality entangled states from low quality entangled states. In this paper, we present the first entanglement purification protocol (EPP) for time-bin entanglement. We first explain this EPP for two-photon time-bin entangled state and then extend it to the system of multi-photon time-bin entangled state. We also design a possible realization of this EPP with practical spontaneous parametric down conversion (SPDC) source. Differ from the conventional EPPs, this EPP does not require the sophisticated controlled-not (CNOT) gate or similar operations, and it uses the feasible sum-frequency generation (SFG) to perform the purification. Moreover, the double-pair noise emitted from the SPDC source can be eliminated automatically which is the other advantage of this EPP. If we combine with the faithful entanglement swapping, this EPP may have potential to be a part of full quantum repeaters.
Entanglement purification is to distill the high quality entanglement from the low quality entanglement with local operations and classical communications. It is one of the key technologies in long-distance quantum communication. We discuss an entanglement purification protocol (EPP) with spontaneous parametric down conversion (SPDC) sources, in contrast to previous EPP with multi-copy mixed states, which requires ideal entanglement sources. We show that the SPDC source is not an obstacle for purification, but can benefit the fidelity of the purified mixed state. This EPP works for linear optics and is feasible in current experiment technology.
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.
Multipartite entanglement plays an important role in controlled quantum teleportation, quantum secret sharing, quantum metrology and some other important quantum information branches. However, the maximally multipartite entangled state will degrade into the mixed state because of the noise. We present an efficient multipartite entanglement purification protocol (EPP) which can distill the high quality entangled states from low quality entangled states for N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state in only linear optics. After performing the protocol, the spatial-mode entanglement is used to purify the polarization entanglement and one pair of high quality polarization entangled state will be obtained. This EPP has several advantages. Firstly, with the same purification success probability, this EPP only requires one pair of multipartite GHZ state, while existing EPPs usually require two pairs of multipartite GHZ state. Secondly, if consider the practical transmission and detector efficiency, this EPP may be extremely useful for the ratio of purification efficiency is increased rapidly with both the number of photons and the transmission distance. Thirdly, this protocol requires linear optics and does not add additional measurement operations, so that it is feasible for experiment. All these advantages will make this protocol have potential application for future quantum information processing.
The entangled coherent states (ECSs) have been widely used to realize quantum information processing tasks. However, the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel, which may degrade the fidelity of ECSs. To overcome these obstacles, we present a measurement-based entanglement purification protocol (MBEPP) for ECSs to distill some high-quality ECSs from a large number of low-quality copies. We first show the principle of this MBEPP without considering the photon loss. After that, we prove that this MBEPP is feasible to correct the error resulted from the photon loss. Additionally, this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications. This MBEPP may have application potential in the implementation of long-distance quantum communication.
Abstract Hybrid entangled states (HESs), which involve different particles with various degrees of freedom, have garnered significant attention and been applied in a wide range of quantum technologies. However, similar to other categories of entanglement, maximally HESs inevitably degrade to mixed states due to the environmental noise and operational imperfections. To address the degradation problem, measurement-based entanglement purification offers a feasible and robust solution alternative to conventional gate-based purification methods. In this paper, we propose a measurement-based hybrid entanglement purification protocol (MB-HEPP) for a certain kind of HES which consists of polarization photons and coherent states. We extend our methodology to several conditions, such as the multi-copy and multi-party scenarios, and the photon-loss condition. Compared with previous HEPPs, this protocol has several advantages. First, it does not depend on post-selection and the purified HESs can be retained for further application. Second, it does not require the Bell state measurement, but only uses the parity check with conventional linear optical elements, which makes it have the higher success probability and more feasible. Our MB-HEPP has potential applications in future heterogeneous quantum networks.