Routing Protocol for Quantum Multicast Networks Based on Hyperentangled Relays

Lei Xing; Guang Yang; Min Nie; Yuanhua Liu; Meiling Zhang

doi:10.3788/LOP213228

Journals >Laser & Optoelectronics Progress >Volume 60 >Issue 7 >Page 0727001 > Article

Laser & Optoelectronics Progress
Vol. 60, Issue 7, 0727001 (2023)

Routing Protocol for Quantum Multicast Networks Based on Hyperentangled Relays

Lei Xing^*, Guang Yang, Min Nie, Yuanhua Liu, and Meiling Zhang

Author Affiliations

School of Communication and Information Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, Shaanxi, China

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DOI: 10.3788/LOP213228 Cite this Article Set citation alerts

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 Copy Citation Text

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Fig. 1. Principle of simultaneous hyperentanglement swapping based on hyperentangled relay

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Fig. 2. Relationship between the number of clone state and fidelity

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Fig. 3. Diamond quantum network model based on hyperentangled relay

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

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

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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