Two-Hierarchy Entanglement Swapping for a Linear Optical Quantum Repeater

Ping Xu, Hai-Lin Yong, Luo-Kan Chen, Chang Liu, Tong Xiang, Xing-Can Yao, He Lu, Zheng-Da Li, Nai-Le Liu, Li Li, Tao Yang, Cheng-Zhi Peng, Bo Zhao, Yu-Ao Chen, and Jian-Wei Pan

Phys. Rev. Lett. 119, 170502 – Published 23 October 2017

Abstract

Quantum repeaters play a significant role in achieving long-distance quantum communication. In the past decades, tremendous effort has been devoted towards constructing a quantum repeater. As one of the crucial elements, entanglement has been created in different memory systems via entanglement swapping. The realization of $j$ -hierarchy entanglement swapping, i.e., connecting quantum memory and further extending the communication distance, is important for implementing a practical quantum repeater. Here, we report the first demonstration of a fault-tolerant two-hierarchy entanglement swapping with linear optics using parametric down-conversion sources. In the experiment, the dominant or most probable noise terms in the one-hierarchy entanglement swapping, which is on the same order of magnitude as the desired state and prevents further entanglement connections, are automatically washed out by a proper design of the detection setting, and the communication distance can be extended. Given suitable quantum memory, our techniques can be directly applied to implementing an atomic ensemble based quantum repeater, and are of significant importance in the scalable quantum information processing.

Received 16 January 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.170502

Physics Subject Headings (PhySH)

Quantum communication Quantum entanglement Quantum information with atoms & light Quantum memories Quantum optics Second order nonlinear optical processes

Atomic, Molecular & OpticalQuantum Information, Science & Technology

Authors & Affiliations

Ping Xu^1,2,3, Hai-Lin Yong^1,2,3, Luo-Kan Chen^1,2,3, Chang Liu^1,2,3, Tong Xiang⁴, Xing-Can Yao^1,2,3, He Lu^1,2,3, Zheng-Da Li^1,2,3, Nai-Le Liu^1,2,3, Li Li^1,2,3, Tao Yang^1,2,3, Cheng-Zhi Peng^1,2,3, Bo Zhao^1,2,3, Yu-Ao Chen^1,2,3, and Jian-Wei Pan^1,2,3

¹Shanghai Branch, National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai 201315, China
²CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai, 201315, China
³CAS-Alibaba Quantum Computing Laboratory, Shanghai, 201315, China
⁴Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240, China

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Vol. 119, Iss. 17 — 27 October 2017

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Images

Figure 1
(a) Schematic view of two-hierarchy entanglement swapping. The neighboring sites $A$ , $B$ , $C$ , and $D$ are separated by $L_{0}$ ; BSM I is performed to demonstrate one-hierarchy entanglement swapping. The resulting state contains noise terms due to the double pair emissions. BSM II is performed between two one-hierarchy entanglement swappings to automatically eliminate the noise terms and heralds the creation of entanglement between photons 1 and 8. (b) The configurations of BSM I and BSM II. The BSM is composed of PBSs and single-photon counting modules. The normal (circular) PBS transmits $H$ ( $+$ ) and reflects $V$ ( $-$ ) photons, where $H$ , $V$ , $+$ , and $-$ represent horizontal, vertical, diagonal, and antidiagonal polarization states, respectively, while $| \pm ⟩ = (| H ⟩ \pm | V ⟩) / \sqrt{2}$ . Both BSM I and BSM II are able to identify the entangled state $| ϕ^{+} ⟩ = (| H ⟩ | H ⟩ + | V ⟩ | V ⟩) / \sqrt{2}$ (see the Supplemental Material [27]). The circular PBS can be achieved by inserting half-wave plates oriented at 22.5° into each port of a normal PBS.
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Figure 2
Experimental setup for the two-hierarchy entanglement swapping. (a) Schematic view of two-hierarchy entanglement swapping. An ultraviolet pump laser (not shown) passes through four BBO crystals to create four entangled photon pairs. Photons 2–7 are subject to BSM I and BSM II to implement the two-hierarchy entanglement swapping. The gray boxes labeled as $d_{1} - d_{8}$ are our detection systems. Photons 1 and 8 are delayed by the optical fibers before the EOM-based unitary operations are ready. (b) Optical setup to generate the entangled photon pairs. We apply the architecture of Bell-state synthesizers to obtain the entangled photon pairs [41]. (c) Detection system. The polarization of each output photon is analyzed by a quarter-wave plate (QWP), a half-wave plate (HWP), a PBS, and two commercial single-photon counting modules with an average quantum efficiency of 64%. (d) Optical elements appearing in our experimental setup.
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Figure 3
Results of two-hierarchy entanglement swapping. (a) The visibility of the heralded two-photon state $ρ_{18}$ under various attenuations in the paths of photons 3 and 6. We conditionally choose the case that only one photon is detected in each site. The coincidence counting events in the $H / V$ , $+ / -$ , and $L / R$ bases are 120, 120, 120 for transmittances of 100% and 73.3%, and 51, 120, 41 for the transmittance of 47.8% (A transmittance of 100% means the attenuators are not inserted.) For the transmittance of 33.5%, we only measure 43 coincidence counting events in the $\pm$ basis because of the too low eightfold coincidence counting rate ( $\sim$ one click per three hours). (b) Heralded probability $p_{2}$ of the two-photon entangled state under various attenuations. The dots denote the experimental results; the probabilities are 0.37, 0.47, 0.63, and 0.85 for transmittances of 100%, 73.3%, 47.8%, and 33.5% in the paths of photons 3 and 6. The dotted line is estimated in the ideal case that only four photon pairs are generated. The solid line is calculated by considering higher-order emissions, where five photon pair generation is considered (Supplemental Material [27]). According to the theory and experiment, the heralded probability $p_{2}$ can definitely be improved when the attenuations on paths 3 and 6 are increased.
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