E-Payment Protocols Based on Quantum Walk

Yefeng He; Mengmei Yang; Zhi Li; Yan Liu; Zheming Tian

doi:10.3788/AOS221642

Journals >Acta Optica Sinica >Volume 43 >Issue 5 >Page 0527001 > Article

Acta Optica Sinica
Vol. 43, Issue 5, 0527001 (2023)

E-Payment Protocols Based on Quantum Walk

Yefeng He, Mengmei Yang^*, Zhi Li, Yan Liu, and Zheming Tian

Author Affiliations

School of Cyberspace Security, Xi'an University of Posts & Telecommunications, Xi'an 710121, Shaanxi, China

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DOI: 10.3788/AOS221642 Cite this Article Set citation alerts

Yefeng He, Mengmei Yang, Zhi Li, Yan Liu, Zheming Tian. E-Payment Protocols Based on Quantum Walk[J]. Acta Optica Sinica, 2023, 43(5): 0527001 Copy Citation Text

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Fig. 1. Protocol model

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Fig. 2. Schematic diagram of quantum-state transmission

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Fig. 3. Probability of Bob1 inferring the contents of the shopping list

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Q-basis	$λ_{2}$	X-basis	$λ_{1}$
$\|1〉$	$1$	$\|+〉$	$1$
$\|2^{'}〉$	$- 1$	$\|-〉$	- $1$
$\|0〉$	$0$
$\|- 1〉$	$- 1$
$\|- 2^{'}〉$	$- 1$

Table 1. Coding of Alice's measurement results

$A_{1}$	$A_{P}$	Revise operation
$1 (- 1)$	$1 (- 1)$	$I$
$1 (- 1)$	$- 1 (1)$	$σ_{z}$
$1$	$0$	$σ_{x}$
$- 1$	$0$	$σ_{z} σ_{x}$

Table 2. Revise Pauli operation

$L_{i}$	$m_{i}$	$\|a_{i} b_{i} c_{i}〉$
$0$	$00$	$\|000〉$ or $\|111〉$
	$01$	$\|001〉$ or $\|110〉$
	$10$	$\|011〉$ or $\|100〉$
	$11$	$\|010〉$ or $\|101〉$
$1$	$00$	$\|+ + +〉$ or $\|- - -〉$
	$01$	$\|+ + -〉$ or $\|- - +〉$
	$10$	$\|+ - -〉$ or $\|- - +〉$
	$11$	$\|+ - +〉$ or $\|- + -〉$

Table 3. Coding rules for purchase information

Protocol	Protocol in Ref.［11］	Protocol in Ref.［13］	Our protocol
Quantum resource	3-particle entangled states，single-particle states	3-particle partial X-LIOP states	Single-particle states
Trusted third party	No	Yes	Yes
Measurements	Bell-state measurements，Single-particle measurements	Single-particle measurements	Single-particle measurements

Table 4. Comparison of relevant protocols

Yefeng He, Mengmei Yang, Zhi Li, Yan Liu, Zheming Tian. E-Payment Protocols Based on Quantum Walk[J]. Acta Optica Sinica, 2023, 43(5): 0527001

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