Routing Protocol for Quantum Multicast Networks Based on Hyperentangled Relays

Fig. 4. Multicast tree set based on hyperentangled relay. (a) Multicast tree $t_{1}$ ; (b) multicast tree $t_{2}$ ; (c) multicast tree $t_{3}$ ; (d) multicast tree $t_{4}$

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Fig. 5. Relationship between clone state fidelity and the number of destination nodes

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Fig. 6. Relationship between entanglement swapping delay of multicast communication and number of relay nodes

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Fig. 7. Relationship between quantum state transmission rate and number of relay nodes

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Table 1. Unitary operations of Bob in N-hop simultaneous hyperentanglement swapping

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Table 1. Unitary operations of Bob in N-hop simultaneous hyperentanglement swapping

Measurement results of R₁ to R_k_-1	Bob’s operation on his particle
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{1} = σ_{P}^{I} \otimes σ_{S}^{I}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{2} = σ_{P}^{I} \otimes σ_{S}^{Z}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{3} = σ_{P}^{I} \otimes σ_{S}^{X}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{4} = σ_{P}^{I} \otimes σ_{S}^{- Y}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{5} = σ_{P}^{Z} \otimes σ_{S}^{I}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{6} = σ_{P}^{Z} \otimes σ_{S}^{Z}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{7} = σ_{P}^{Z} \otimes σ_{S}^{X}$
$\bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{8} = σ_{P}^{Z} \otimes σ_{S}^{- Y}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{9} = σ_{P}^{X} \otimes σ_{S}^{I}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{10} = σ_{P}^{X} \otimes σ_{S}^{Z}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{11} = σ_{P}^{X} \otimes σ_{S}^{X}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{P}^{k 2}} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{12} = σ_{P}^{X} \otimes σ_{S}^{- Y}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{13} = σ_{P}^{- Y} \otimes σ_{S}^{I}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 1}} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{14} = σ_{P}^{- Y} \otimes σ_{S}^{Z}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \bar{\oplus_{k = 1}^{N - 1} M_{S}^{k 2}} = 1$	$U_{15} = σ_{P}^{- Y} \otimes σ_{S}^{X}$
$\oplus_{k = 1}^{N - 1} M_{P}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{P}^{k 2} \otimes \oplus_{k = 1}^{N - 1} M_{S}^{k 1} \cdot \oplus_{k = 1}^{N - 1} M_{S}^{k 2} = 1$	$U_{16} = σ_{P}^{- Y} \otimes σ_{S}^{- Y}$

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Lei Xing, Guang Yang, Min Nie, Yuanhua Liu, Meiling Zhang. Routing Protocol for Quantum Multicast Networks Based on Hyperentangled Relays[J]. Laser & Optoelectronics Progress, 2023, 60(7): 0727001

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Paper Information

Category: Quantum Optics

Received: Dec. 14, 2021

Accepted: Jan. 26, 2022

Published Online: Mar. 31, 2023

The Author Email: Xing Lei (1141127606@qq.com)

DOI:10.3788/LOP213228

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology