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

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 7 >Page 0727002 > Article

Laser & Optoelectronics Progress
Vol. 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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DOI: 10.3788/LOP202158.0727002 Cite this Article Set citation alerts

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 Copy Citation Text

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

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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 1. Quantum logic gates and corresponding quantum states

			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 2. Validation rules


$\|+〉$	$\|ϕ^{+}〉$	$\|ϕ^{+}〉$	00
$\|-〉$	$\|ϕ^{+}〉$	$\|ψ^{-}〉$	10
$\|+〉$	$\|ϕ^{-}〉$	$\|ϕ^{-}〉$	00

Table 3. Measurement results and recovery bits

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%

Table 4. Comparison of protocols

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