Recycling nonlocality in quantum star networks

Open Access

Recycling nonlocality in quantum star networks

Ya-Li Mao, Zheng-Da Li, Anna Steffinlongo, Bixiang Guo, Biyao Liu, Shufeng Xu, Nicolas Gisin, Armin Tavakoli, and Jingyun Fan

Phys. Rev. Research 5, 013104 – Published 13 February 2023

Abstract

The nonlocality of an entangled qubit pair can be recycled for several Bell experiments. Here, we go beyond standard Bell scenarios and investigate the recycling of nonlocal resources in a quantum network. First, we show that the ability to recycle nonlocality can be independent of the size of the network. Then, we realize a photonic quantum three-branch star network in which three sources of entangled pairs independently connect three outer parties with a central node. After measuring, each outer party respectively relays their system to an independent secondary measuring party. We experimentally demonstrate that the outer parties can perform unsharp measurements that are strong enough to violate a network Bell inequality with the central party, but weak enough to maintain sufficient entanglement in the network to allow the three secondary parties to do the same. Moreover, the violations are strong enough to exclude any model based on standard projective measurements on the Einstein-Podolsky-Rosen pairs emitted in the network. Our experiment brings together the research program of recycling quantum resources with that of Bell nonlocality in networks.

Received 21 February 2022
Accepted 24 January 2023

DOI:https://doi.org/10.1103/PhysRevResearch.5.013104

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlocality Quantum correlations in quantum information Quantum entanglement Quantum networks

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Ya-Li Mao^1,2,*, Zheng-Da Li^1,2,*, Anna Steffinlongo^3,4,5, Bixiang Guo^1,2, Biyao Liu^1,2, Shufeng Xu^1,2, Nicolas Gisin^6,7,†, Armin Tavakoli^4,5,‡, and Jingyun Fan ^1,2,8,§

¹Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
²Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
³Dipartimento di Fisica e Astronomia “G. Galilei,” Università degli Studi di Padova, I-35131 Padua, Italy
⁴Institute for Quantum Optics and Quantum Information - IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
⁵Atominstitut, Technische Universität Wien, Stadionallee 2, A-1020 Vienna, Austria
⁶Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
⁷Constructor University, 1211 Geneva 4, Switzerland
⁸Center for Advanced Light Source, Southern University of Science and Technology, Shenzhen 518055, China

^*These authors contributed equally to this work.
^†Nicolas.gisin@unige.ch
^‡armin.tavakoli@teorfys.lu.se
^§fanjy@sustech.edu.cn

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Vol. 5, Iss. 1 — February - April 2023

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Figure 1
Scenario: Recycling one share of each of the $m$ independent entangled states in a quantum star network with the aim that any selection of $m$ parties (one from each branch) can violate a star-network Bell inequality with Alice.
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Figure 1
Scenario: Recycling one share of each of the $m$ independent entangled states in a quantum star network with the aim that any selection of $m$ parties (one from each branch) can violate a star-network Bell inequality with Alice.
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Figure 2
Experimental schematic of recycling nonlocality in a quantum network. (a) We split a UV laser pulse with a pulse duration of $τ = 150$ fs and $λ = 390$ nm into three pulses of equal energy. (b) Each pulse induces SPDC in a pair of BBO crystals (with a HWP in between) to probabilistically emit a pair of photons at $λ = 780$ nm in the Bell state $| Φ^{+} 〉$ [63, 64, 65] as the independent source. Pairs of spatial compensation (SC)- ${YVO}_{4}$ and temporal compensation (TC)- ${YVO}_{4}$ crystals are used to remove spatial and temporal walk-offs due to orthogonally polarized photons traversing BBO. (c) Party $A$ is connected to three branches via three sources. In each branch, party $B_{k, 1}$ performs an unsharp measurement to the photon and then relays the photon to party $B_{k, 2}$ . The unsharp measurement is implemented in a Sagnac interferometer, in which the photon in polarization states $| H 〉$ and $| V 〉$ travels along separate spatial paths. We use a HWP to vary the coupling between the polarization degree of freedom and the path degree of freedom to adjust the unsharp measurement $η_{k, 1}^{X} σ_{X}$ or $η_{k, 1}^{Z} σ_{Z}$ . We use a QHQ box, i.e., a quarter-wave plate (QWP), a HWP, and another QWP in series, to set a photon to any polarization state on a Bloch sphere. Party $B_{k, 2}$ uses a HWP, a QWP, and a polarizing beamsplitters (PBS) to perform a projective polarization measurement to single photons and send them to detectors via an optical fiber. All photon detection events are time tagged for correlation analysis (not shown).
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Figure 2
Experimental schematic of recycling nonlocality in a quantum network. (a) We split a UV laser pulse with a pulse duration of $τ = 150$ fs and $λ = 390$ nm into three pulses of equal energy. (b) Each pulse induces SPDC in a pair of BBO crystals (with a HWP in between) to probabilistically emit a pair of photons at $λ = 780$ nm in the Bell state $| Φ^{+} 〉$ [63, 64, 65] as the independent source. Pairs of spatial compensation (SC)- ${YVO}_{4}$ and temporal compensation (TC)- ${YVO}_{4}$ crystals are used to remove spatial and temporal walk-offs due to orthogonally polarized photons traversing BBO. (c) Party $A$ is connected to three branches via three sources. In each branch, party $B_{k, 1}$ performs an unsharp measurement to the photon and then relays the photon to party $B_{k, 2}$ . The unsharp measurement is implemented in a Sagnac interferometer, in which the photon in polarization states $| H 〉$ and $| V 〉$ travels along separate spatial paths. We use a HWP to vary the coupling between the polarization degree of freedom and the path degree of freedom to adjust the unsharp measurement $η_{k, 1}^{X} σ_{X}$ or $η_{k, 1}^{Z} σ_{Z}$ . We use a QHQ box, i.e., a quarter-wave plate (QWP), a HWP, and another QWP in series, to set a photon to any polarization state on a Bloch sphere. Party $B_{k, 2}$ uses a HWP, a QWP, and a polarizing beamsplitters (PBS) to perform a projective polarization measurement to single photons and send them to detectors via an optical fiber. All photon detection events are time tagged for correlation analysis (not shown).
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Figure 3
Simultaneous experimental violations of network Bell inequality (3) with any choice of three or two outer parties from separate branches together with party $A$ in (a) and (b), respectively, where $*$ represents the branch unused in the respective study. Error bars shown in (a) and (b) represent one standard deviation in the experiment.
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Figure 4
Experimental sequential test of CHSH-Bell inequality in each branch ( $k = 1, 2, 3$ ). The ${CHSH}_{1}$ ( ${CHSH}_{2}$ ) is measured between $A$ and $B_{k, 1}$ ( $B_{k, 2}$ ). The three measured double values are $(2.1834 \pm 0.0116, 2.1997 \pm 0.0074)$ , $(2.1755 \pm 0.0114, 2.1072 \pm 0.0075)$ , and $(2.1685 \pm 0.0114, 2.1991 \pm 0.0073)$ , illustrated by the open dot, solid dot, and open square, respectively. Error bars represent one standard deviation. The dashed line represents the optimal trade-off based on projective measurements and shared randomness. The solid line is the local model bound.
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