Protocol of Quantum Blind Signature Based on Two-Qubit and Three-Qubit Maximally Entangled States

Junhui Wang; Yunxia Li; Wen Meng; Jiahua Wei; Jie Tang; Tianxiong Wu

doi:10.3788/LOP202158.0727002

Laser & Optoelectronics Progress, Volume. 58, Issue 7, 0727002(2021)

Protocol of Quantum Blind Signature Based on Two-Qubit and Three-Qubit Maximally Entangled States

Junhui Wang, Yunxia Li^*, Wen Meng^**, Jiahua Wei^***, Jie Tang, and Tianxiong Wu

Author Affiliations

Information and Navigation College, Air Force Engineering University, Xi'an , Shaanxi 710077, China

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Abstract Get PDF(in Chinese)

Figures & Tables(5)

Fig. 1. Schematic of quantum distribution. (a) Initial state; (b) states after distribution

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Table 1. Quantum logic gates and corresponding quantum states
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Table 1. Quantum logic gates and corresponding quantum states
Operation on particle A Primitive quantum state Post-operation quantum state
$I$ ${|ϕ^{+}〉}_{A B}$ ${|ϕ^{+}〉}_{A B}$
$σ_{X}$ ${|ϕ^{+}〉}_{A B}$ ${|ψ^{+}〉}_{A B}$
$σ_{Z}$ ${|ϕ^{+}〉}_{A B}$ ${|ϕ^{-}〉}_{A B}$
$i σ_{Y}$ ${|ϕ^{+}〉}_{A B}$ ${|ψ^{-}〉}_{A B}$

Table 2. Validation rules

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Table 2. Validation rules

			Operation on particle A					Operation on particle A
$\|ϕ^{+}〉$	$\|ϕ^{+}〉$	$\|+〉$	$I$	00	$\|ϕ^{-}〉$	$\|ϕ^{+}〉$	$\|+〉$	$σ_{Z}$	01
$\|ϕ^{+}〉$	$\|ϕ^{+}〉$	$\|-〉$	$σ_{Z}$	01	$\|ϕ^{-}〉$	$\|ϕ^{+}〉$	$\|-〉$	$I$	00
$\|ϕ^{+}〉$	$\|ϕ^{-}〉$	$\|+〉$	$σ_{Z}$	01	$\|ϕ^{-}〉$	$\|ϕ^{-}〉$	$\|+〉$	$I$	00
$\|ϕ^{+}〉$	$\|ϕ^{-}〉$	$\|-〉$	$I$	00	$\|ϕ^{-}〉$	$\|ϕ^{-}〉$	$\|-〉$	$σ_{Z}$	01
$\|ϕ^{+}〉$	$\|ψ^{+}〉$	$\|+〉$	$I$	00	$\|ϕ^{-}〉$	$\|ψ^{+}〉$	$\|+〉$	$σ_{Z}$	01
$\|ϕ^{+}〉$	$\|ψ^{+}〉$	$\|-〉$	$σ_{Z}$	01	$\|ϕ^{-}〉$	$\|ψ^{+}〉$	$\|-〉$	$I$	00
$\|ϕ^{+}〉$	$\|ψ^{-}〉$	$\|+〉$	$σ_{Z}$	01	$\|ϕ^{-}〉$	$\|ψ^{-}〉$	$\|+〉$	$I$	00
$\|ϕ^{+}〉$	$\|ψ^{-}〉$	$\|-〉$	$I$	00	$\|ϕ^{-}〉$	$\|ψ^{-}〉$	$\|-〉$	$σ_{Z}$	01
$\|ψ^{+}〉$	$\|ϕ^{+}〉$	$\|+〉$	$i σ_{Y}$	10	$\|ψ^{-}〉$	$\|ϕ^{+}〉$	$\|+〉$	$σ_{X}$	11
$\|ψ^{+}〉$	$\|ϕ^{+}〉$	$\|-〉$	$σ_{X}$	11	$\|ψ^{-}〉$	$\|ϕ^{+}〉$	$\|-〉$	$i σ_{Y}$	10
$\|ψ^{+}〉$	$\|ϕ^{-}〉$	$\|+〉$	$σ_{X}$	11	$\|ψ^{-}〉$	$\|ϕ^{-}〉$	$\|+〉$	$i σ_{Y}$	10
$\|ψ^{+}〉$	$\|ϕ^{-}〉$	$\|-〉$	$i σ_{Y}$	10	$\|ψ^{-}〉$	$\|ϕ^{-}〉$	$\|-〉$	$σ_{X}$	11
$\|ψ^{+}〉$	$\|ψ^{+}〉$	$\|+〉$	$i σ_{Y}$	10	$\|ψ^{-}〉$	$\|ψ^{+}〉$	$\|+〉$	$σ_{X}$	11
$\|ψ^{+}〉$	$\|ψ^{+}〉$	$\|-〉$	$σ_{X}$	11	$\|ψ^{-}〉$	$\|ψ^{+}〉$	$\|-〉$	$i σ_{Y}$	10
$\|ψ^{+}〉$	$\|ψ^{-}〉$	$\|+〉$	$σ_{X}$	11	$\|ψ^{-}〉$	$\|ψ^{-}〉$	$\|+〉$	$i σ_{Y}$	10
$\|ψ^{+}〉$	$\|ψ^{-}〉$	$\|-〉$	$i σ_{Y}$	10	$\|ψ^{-}〉$	$\|ψ^{-}〉$	$\|-〉$	$σ_{X}$	11

Table 3. Measurement results and recovery bits
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Table 3. Measurement results and recovery bits
$|+〉$ $|ϕ^{+}〉$ $|ϕ^{+}〉$ 00
$|-〉$ $|ϕ^{+}〉$ $|ψ^{-}〉$ 10
$|+〉$ $|ϕ^{-}〉$ $|ϕ^{-}〉$ 00

Table 4. Comparison of protocols

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Table 4. Comparison of protocols

Parameter	Protocol in Ref.[17]	Protocol in Ref.[16]	Proposed protocol
Quantum resource	$n$ five-qubit entangled states	$3 n$ hybrid entangled states	$⌈\frac{n}{2}⌉$ Bell states and $⌈\frac{n}{2}⌉$ GHz states
Measurement basis	GHz basis and Bell basis	Hybrid entangled basis	Bell basis and single photon basis
Verification method	Two-level comparison	One-level comparison	One-level comparison
Signature efficiency	20%	33.3%	40%

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Junhui Wang, Yunxia Li, Wen Meng, Jiahua Wei, Jie Tang, Tianxiong Wu. Protocol of Quantum Blind Signature Based on Two-Qubit and Three-Qubit Maximally Entangled States[J]. Laser & Optoelectronics Progress, 2021, 58(7): 0727002

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