Quantum key distribution using polarization and frequency hyperentangled photons

Chuan Wang; Li Xiao; Wan-ying Wang; Guang-yu Zhang; Gui Lu Long

doi:10.1364/JOSAB.26.002072

Journal of the Optical Society of America B
Vol. 26,
Issue 11,
pp. 2072-2076
(2009)
•https://doi.org/10.1364/JOSAB.26.002072

Quantum key distribution using polarization and frequency hyperentangled photons

Chuan Wang, Li Xiao, Wan-ying Wang, Guang-yu Zhang, and Gui Lu Long

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Chuan Wang, Li Xiao, Wan-ying Wang, Guang-yu Zhang, and Gui Lu Long, "Quantum key distribution using polarization and frequency hyperentangled photons," J. Opt. Soc. Am. B 26, 2072-2076 (2009)

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Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: January 23, 2009
- Revised Manuscript: August 1, 2009
- Manuscript Accepted: September 15, 2009
- Published: October 16, 2009

Abstract

We propose a two-step quantum key distribution protocol using frequency and polarization hyperentangled photons. In this protocol, key information is encoded by unitary operations on the hyperentangled photons, and the hyperentangled photons are sent in two steps. We also designed a state measurement device and analyzed the security of the protocol.

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Key	Operation	State	Key	Operation	State
000	$I \otimes I$	$Ψ^{+}$	100	$σ_{x} \otimes I$	$Υ^{+}$
001	$I \otimes σ_{z}$	$Ψ^{-}$	101	$σ_{x} \otimes σ_{z}$	$Υ^{-}$
010	$I \otimes σ_{x}$	$Φ^{+}$	110	$σ_{x} \otimes σ_{x}$	$Γ^{+}$
011	$I \otimes i σ_{y}$	$Φ^{-}$	111	$σ_{x} \otimes i σ_{y}$	$Γ^{-}$
000	$σ_{z} \otimes σ_{z}$	$Ψ^{+}$	100	$i σ_{y} \otimes σ_{z}$	$Υ^{+}$
001	$σ_{z} \otimes I$	$Ψ^{-}$	101	$i σ_{y} \otimes I$	$Υ^{-}$
010	$σ_{z} \otimes i σ_{y}$	$Φ^{+}$	110	$i σ_{y} \otimes i σ_{y}$	$Γ^{+}$
011	$σ_{z} \otimes σ_{x}$	$Φ^{-}$	111	$i σ_{y} \otimes σ_{x}$	$Γ^{-}$

Triggered Port	Corresponding states
1,2	$\| Φ^{\pm} ⟩$
1,4	$\| Ψ^{\pm} ⟩$
3,2	$\| Γ^{\pm} ⟩$
3,4	$\| Υ^{\pm} ⟩$

Key	Operation	State	Key	Operation	State
000	$I \otimes I$	$Ψ^{+}$	100	$σ_{x} \otimes I$	$Υ^{+}$
001	$I \otimes σ_{z}$	$Ψ^{-}$	101	$σ_{x} \otimes σ_{z}$	$Υ^{-}$
010	$I \otimes σ_{x}$	$Φ^{+}$	110	$σ_{x} \otimes σ_{x}$	$Γ^{+}$
011	$I \otimes i σ_{y}$	$Φ^{-}$	111	$σ_{x} \otimes i σ_{y}$	$Γ^{-}$
000	$σ_{z} \otimes σ_{z}$	$Ψ^{+}$	100	$i σ_{y} \otimes σ_{z}$	$Υ^{+}$
001	$σ_{z} \otimes I$	$Ψ^{-}$	101	$i σ_{y} \otimes I$	$Υ^{-}$
010	$σ_{z} \otimes i σ_{y}$	$Φ^{+}$	110	$i σ_{y} \otimes i σ_{y}$	$Γ^{+}$
011	$σ_{z} \otimes σ_{x}$	$Φ^{-}$	111	$i σ_{y} \otimes σ_{x}$	$Γ^{-}$

Triggered Port	Corresponding states
1,2	$\| Φ^{\pm} ⟩$
1,4	$\| Ψ^{\pm} ⟩$
3,2	$\| Γ^{\pm} ⟩$
3,4	$\| Υ^{\pm} ⟩$

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Journal of the Optical Society of America B