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Two-party quantum key agreement protocols under collective noise channel

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Abstract

Recently, quantum communication has become a very popular research field. The quantum key agreement (QKA) plays an important role in the field of quantum communication, based on its unconditional security in terms of theory. Among all kinds of QKA protocols, QKA protocols resisting collective noise are widely being studied. In this paper, we propose improved two-party QKA protocols resisting collective noise and present a feasible plan for information reconciliation. Our protocols’ qubit efficiency has achieved 26.67%, which is the best among all the two-party QKA protocols against collective noise, thus showing that our protocol can improve the transmission efficiency of quantum key agreement.

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Authors and Affiliations

  1. Department of Communication Science and Engineering, Fudan University, Shanghai, 200433, China

    Hao Gao, Xiao-Guang Chen & Song-Rong Qian

Authors
  1. Hao Gao
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  2. Xiao-Guang Chen
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  3. Song-Rong Qian
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Corresponding author

Correspondence to Hao Gao.

Appendix

Appendix

1.1 Holevo’s bound [18]

Suppose Alice prepares a state \(\rho _X\) where \(X=0, 1, \dots , n\) with probabilities \(p_0, p_1, \dots , p_n\). Bob performs a measurement described by POVM (positive operator-valued measure) elements \(\{E_y \}=\{E_0, E_1,\dots , E_m \}\) on that state, with measurement outcome Y. The Holevo bound states that for any such measurement Bob may do:

$$\begin{aligned} H(X:Y)\le S(\rho )-\sum _x p_xS(\rho _x), \end{aligned}$$
(11)

where \(\rho =\sum _xp_x\rho _x\).

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Gao, H., Chen, XG. & Qian, SR. Two-party quantum key agreement protocols under collective noise channel. Quantum Inf Process 17, 140 (2018). https://doi.org/10.1007/s11128-018-1910-1

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