Multi-hop nondestructive teleportation between terminal nodes equipped with limited technology

Fenxiang Fu; Huayang Li; Shibei Xue; Shibei Xue; Min Jiang; Min Jiang

doi:10.1364/JOSAB.392613

Journal of the Optical Society of America B
Vol. 37,
Issue 6,
pp. 1896-1905
(2020)
•https://doi.org/10.1364/JOSAB.392613

Multi-hop nondestructive teleportation between terminal nodes equipped with limited technology

Fenxiang Fu, Huayang Li, Shibei Xue, and Min Jiang

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Fenxiang Fu, Huayang Li, Shibei Xue, and Min Jiang, "Multi-hop nondestructive teleportation between terminal nodes equipped with limited technology," J. Opt. Soc. Am. B 37, 1896-1905 (2020)

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Abstract

In this paper, we propose a scheme for the multi-hop nondestructive teleportation of an arbitrary single-qudit state via channel modulation performed by one cloud node in a network. Considering the limited quantum technology of the sender, the receiver, and the ordinary intermediate nodes, we assume that there are certain cloud nodes in a quantum network equipped with quantum processing capability of performing high-dimensional multi-qudit unitary operations. In our scheme, $N$ intermediate nodes, involving one cloud node and $N - 1$ ordinary relay nodes, are connected in a chain through $N + 1$ different non-maximally entangled Bell pairs. Our scheme reduces the hardware requirement of the terminals, which makes it more flexible and adaptable in a network. In addition, our scheme enables preservation of the original single-qudit state, even if the teleportation fails. Our finding provides a methodology for the multi-hop nondestructive teleportation in a network with limited technical processing capabilities of terminals.

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Equations (35)

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$\| ϕ_{mn} ⟩_{B_{1} A_{2}}$	$\| φ ⟩_{A_{1} B_{2}}$	$\| ϕ_{mn} ⟩_{B_{3} A_{4}}$	$\| φ ⟩_{A_{3} B_{4}}$
$\| ϕ_{00} ⟩_{B_{1} A_{2}}$	$a_{10} a_{20} \| 00 ⟩ + a_{11} a_{21} \| 11 ⟩ + a_{12} a_{22} \| 22 ⟩$	$\| ϕ_{00} ⟩_{B_{3} A_{4}}$	$a_{30} a_{40} \| 00 ⟩ + a_{31} a_{41} \| 11 ⟩ + a_{32} a_{42} \| 22 ⟩$
$\| ϕ_{10} ⟩_{B_{1} A_{2}}$	$a_{10} a_{20} \| 00 ⟩ + e^{- \frac{2 π i}{3}} a_{11} a_{21} \| 11 ⟩ + e^{- \frac{4 π i}{3}} a_{12} a_{22} \| 22 ⟩$	$\| ϕ_{10} ⟩_{B_{3} A_{4}}$	$a_{30} a_{40} \| 00 ⟩ + e^{- \frac{2 π i}{3}} a_{31} a_{41} \| 11 ⟩ + e^{- \frac{4 π i}{3}} a_{32} a_{42} \| 22 ⟩$
$\| ϕ_{20} ⟩_{B_{1} A_{2}}$	$a_{10} a_{20} \| 00 ⟩ + e^{- \frac{4 π i}{3}} a_{11} a_{21} \| 11 ⟩ + e^{- \frac{8 π i}{3}} a_{12} a_{22} \| 22 ⟩$	$\| ϕ_{20} ⟩_{B_{3} A_{4}}$	$a_{30} a_{40} \| 00 ⟩ + e^{- \frac{4 π i}{3}} a_{31} a_{41} \| 11 ⟩ + e^{- \frac{8 π i}{3}} a_{32} a_{42} \| 22 ⟩$
$\| ϕ_{01} ⟩_{B_{1} A_{2}}$	$a_{10} a_{21} \| 01 ⟩ + a_{11} a_{22} \| 12 ⟩ + a_{12} a_{20} \| 20 ⟩$	$\| ϕ_{01} ⟩_{B_{3} A_{4}}$	$a_{30} a_{41} \| 01 ⟩ + a_{31} a_{42} \| 12 ⟩ + a_{32} a_{40} \| 20 ⟩$
$\| ϕ_{11} ⟩_{B_{1} A_{2}}$	$a_{10} a_{21} \| 01 ⟩ + e^{- \frac{2 π i}{3}} a_{11} a_{22} \| 12 ⟩ + e^{- \frac{4 π i}{3}} a_{12} a_{20} \| 20 ⟩$	$\| ϕ_{11} ⟩_{B_{3} A_{4}}$	$a_{30} a_{41} \| 01 ⟩ + e^{- \frac{2 π i}{3}} a_{31} a_{42} \| 12 ⟩ + e^{- \frac{4 π i}{3}} a_{32} a_{40} \| 20 ⟩$
$\| ϕ_{21} ⟩_{B_{1} A_{2}}$	$a_{10} a_{21} \| 01 ⟩ + e^{- \frac{4 π i}{3}} a_{11} a_{22} \| 12 ⟩ + e^{- \frac{8 π i}{3}} a_{12} a_{20} \| 20 ⟩$	$\| ϕ_{21} ⟩_{B_{3} A_{4}}$	$a_{30} a_{41} \| 01 ⟩ + e^{- \frac{4 π i}{3}} a_{31} a_{42} \| 12 ⟩ + e^{- \frac{8 π i}{3}} a_{32} a_{40} \| 20 ⟩$
$\| ϕ_{02} ⟩_{B_{1} A_{2}}$	$a_{10} a_{22} \| 02 ⟩ + a_{11} a_{20} \| 10 ⟩ + a_{12} a_{21} \| 21 ⟩$	$\| ϕ_{02} ⟩_{B_{3} A_{4}}$	$a_{30} a_{42} \| 02 ⟩ + a_{31} a_{40} \| 10 ⟩ + a_{32} a_{41} \| 21 ⟩$
$\| ϕ_{12} ⟩_{B_{1} A_{2}}$	$a_{10} a_{22} \| 02 ⟩ + e^{- \frac{2 π i}{3}} a_{11} a_{20} \| 10 ⟩ + e^{- \frac{4 π i}{3}} a_{12} a_{21} \| 21 ⟩$	$\| ϕ_{12} ⟩_{B_{3} A_{4}}$	$a_{30} a_{42} \| 02 ⟩ + e^{- \frac{2 π i}{3}} a_{31} a_{40} \| 10 ⟩ + e^{- \frac{4 π i}{3}} a_{32} a_{41} \| 21 ⟩$
$\| ϕ_{22} ⟩_{B_{1} A_{2}}$	$a_{10} a_{22} \| 02 ⟩ + e^{- \frac{4 π i}{3}} a_{11} a_{20} \| 10 ⟩ + e^{- \frac{8 π i}{3}} a_{12} a_{21} \| 21 ⟩$	$\| ϕ_{22} ⟩_{B_{3} A_{4}}$	$a_{30} a_{42} \| 02 ⟩ + e^{- \frac{4 π i}{3}} a_{31} a_{40} \| 10 ⟩ + e^{- \frac{8 π i}{3}} a_{32} a_{41} \| 21 ⟩$

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Equations (35)

Journal of the Optical Society of America B