Electronic Payment Protocol Based on Quantum Dense Coding

Table 1. Relationship between measured results and Alice's operations
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Table 1. Relationship between measured results and Alice's operations
Classicbit Unitaryoperator Charlie'smeasurementresult Bob'smeasurementresult
00 I |0>₂ |φ⁺>
00 I |1>₂ |ψ⁺>
01 σ_x |0>₂ |ψ⁺>
01 σ_x |1>₂ |φ⁺>
10 iσ_y |0>₂ |ψ^->
10 iσ_y |1>₂ |φ^->
11 σ_z |0>₂ |φ^->
11 σ_z |1>₂ |ψ^->

Table 2. Relationship among M'₁, β'_B1, r and β_C

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Table 2. Relationship among M'₁, β'_B1, r and β_C

M'₁	β'_B1	r	β_C
00	0	00	\|φ⁺>
00	0	01	\|ψ⁺>
00	0	10	\|ψ^->
00	0	11	\|φ^->
00	1	00	\|ψ⁺>
00	1	01	\|φ⁺>
00	1	10	\|φ^->
00	1	11	\|ψ^->
01	0	00	\|ψ⁺>
01	0	01	\|φ⁺>
01	0	10	\|φ^->
01	0	11	\|ψ^->
01	1	00	\|φ⁺>
01	1	01	\|ψ⁺>
01	1	10	\|ψ^->
01	1	11	\|φ^->
10	0	00	\|ψ^->
10	0	01	\|φ^->
10	0	10	\|φ⁺>
10	0	11	\|ψ⁺>
10	1	00	\|φ^->
10	1	01	\|ψ^->
10	1	10	\|ψ⁺>
10	1	11	\|φ⁺>
11	0	00	\|φ^->
11	0	01	\|ψ^->
11	0	10	\|ψ⁺>
11	0	11	\|φ⁺>
11	1	00	\|ψ^->
11	1	01	\|φ^->
11	1	10	\|φ⁺>
11	1	11	\|ψ⁺>

Table 3. Comparison between proposed protocol and others

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Table 3. Comparison between proposed protocol and others

Method	Quantum resource	Measurement	Controlledteleportation	Unitaryoperator
Protocol in Ref.[7]	Genuinely entangledsix-qubit state	Three Bell statemeasurement	Yes	Once
Protocol in Ref.[8]	Six-qubitentangled state	One single particle measurement, one GHZ state measurement, and one Bell state measurement	Yes	Once
Protocol in Ref.[9]	Four-particlecluster state	Two Bell statemeasurement	Yes	Once
Proposed protocol	Three-particleentangled state	One single particle measurement,and one Bell state measurement	No	Twice

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Yefeng He, Sihao Chen, Yuwei Qiang, Lina Li, Qian Bai. Electronic Payment Protocol Based on Quantum Dense Coding[J]. Acta Optica Sinica, 2021, 41(10): 1027001

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