Quantum Key Agreement Protocols Immune to Collective Noise

Table 1. Bit string and its corresponding state
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Table 1. Bit string and its corresponding state
${C^{l}}_{A}$ { $q_{3}^{i}$ , $q_{4}^{i}$ }
00 |00>
01 |01>
10 |10>
11 |11>

Table 2. Measurement result and its corresponding value
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Table 2. Measurement result and its corresponding value
Measurement result of Bob Measurement result of Alice Value of C^l_A Raw key M
|G₁> |+> 00 000
|G₂> |-> 00 001
|G₁> |+> 01 010
|G₂> |-> 01 011
|G₃> |+> 10 100
|G₄> |-> 10 101
|G₃> |+> 11 110
|G₄> |-> 11 111

Table 3. Unitary operation and its transformation result
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Table 3. Unitary operation and its transformation result
Initial state U₀₀ U₀₁ U₁₀ U₁₁
|+> |+> |-> |0> |1>
|-> |-> |+> |1> |0>

Table 4. Transformation rule of state |Ψ⁺>
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Table 4. Transformation rule of state |Ψ⁺>
Initial state Unitary operation Final state
|Ψ⁺> U₀₀􀱋U₀₀ |Ψ⁺>
U₁₁􀱋U₀₁ |Ψ^->

Table 5. Decoding table
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Table 5. Decoding table
Measurement result of Bob Measurement result of Alice ${q_{3}^{i}, q_{4}^{i}}$ Raw key M
|L₁> |+> |Φ⁺> 000
|L₂> |-> |Φ⁺> 001
|L₁> |+> |Φ^-> 010
|L₂> |-> |Φ^-> 011
|L₃> |+> |Ψ⁺> 100
|L₄> |-> |Ψ⁺> 101
|L₃> |+> |Ψ^-> 110
|L₄> |-> |Ψ^-> 111

Table 6. Comparison between proposed protocols and other protocols

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Table 6. Comparison between proposed protocols and other protocols

QKA protocol	Quantum resource	Quantum measurement basis	Qubit efficiency /%
Method in Ref. [8]	Logical Bell state	Z-basis and X-basis	16.67
Method in Ref. [9]	Logical χ state	ZZ-basis and Bell-basis	21.05
Method in Ref. [10]	Logical Bell state	X-basis and Bell-basis	26.67
Method in Ref. [12]	Logical χ state	Bell-basis	20.00
Method in Ref. [13]	Logical Bell state	Bell-basis	25.00
Proposed protocol	Logical Bell state	X-basis and Bell-basis	27.27

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Jie Tang, Lei Shi, Jiahua Wei, Huicun Yu, Tianxiong Wu, Yang Xue. Quantum Key Agreement Protocols Immune to Collective Noise[J]. Laser & Optoelectronics Progress, 2020, 57(17): 172703

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