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Effect of noise on deterministic joint remote preparation of an arbitrary two-qubit state

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Abstract

Quantum communication has attracted much attention in recent years. Deterministic joint remote state preparation (DJRSP) is an important branch of quantum secure communication which could securely transmit a quantum state with 100% success probability. In this paper, we study DJRSP of an arbitrary two-qubit state in noisy environment. Taking a GHZ based DJRSP scheme of a two-qubit state as an example, we study how the scheme is influenced by all types of noise usually encountered in real-world implementations of quantum communication protocols, i.e., the bit-flip, phase-flip (phase-damping), depolarizing, and amplitude-damping noise. We demonstrate that there are four different output states in the amplitude-damping noise, while there is the same output state in each of the other three types of noise. The state-independent average fidelity is presented to measure the effect of noise, and it is shown that the depolarizing noise has the worst effect on the DJRSP scheme, while the amplitude-damping noise or the phase-flip has the slightest effect depending on the noise rate. Our results are also suitable for JRSP and RSP.

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Acknowledgements

This project was supported by the National Natural Science Foundation of China (Grant Nos. 61601358, 61373131), the Natural Science Foundation of Shaanxi Province (2016JM6030), the Scientific Research Program Funded by Shaanxi Provincial Education Department (15JK1317), PAPD and CICAEET.

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Authors and Affiliations

  1. School of Computer Science, Xi’an Polytechnic University, Xi’an, 710048, China

    Ming-Ming Wang, Wei Wang & Jin-Guang Chen

  2. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Ming-Ming Wang & Zhi-Guo Qu

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  1. Ming-Ming Wang
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  2. Zhi-Guo Qu
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  3. Wei Wang
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Correspondence to Ming-Ming Wang.

Appendix

Appendix

$$\begin{aligned} \begin{aligned} V_0&=\frac{1}{2} \left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c} 1 &{} { e^{- i \theta _1} } &{} { e^{- i \theta _2} } &{} { e^{- i \theta _3} } \\ 1 &{} { -e^{- i \theta _1} } &{} { e^{- i \theta _2} } &{} { -e^{- i \theta _3} } \\ 1 &{} { -e^{- i \theta _1} } &{} { -e^{- i \theta _2} } &{} { e^{- i \theta _3} } \\ 1 &{} { e^{- i \theta _1} } &{} { -e^{- i \theta _2} } &{} { -e^{- i \theta _3} } \end{array}\right) ,\quad V_1=\frac{1}{2} \left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c} { e^{- i \theta _1} } &{} 1 &{} { e^{- i \theta _3} } &{} { e^{- i \theta _2} } \\ { -e^{- i \theta _1}} &{} 1 &{} { -e^{- i \theta _3}} &{} { e^{- i \theta _2} } \\ { -e^{- i \theta _1}} &{} 1 &{} { e^{- i \theta _3} } &{} { -e^{- i \theta _2} } \\ { e^{- i \theta _1} } &{} 1 &{} { -e^{- i \theta _3}} &{} { -e^{- i \theta _2} } \end{array}\right) ,\\ V_2&=\frac{1}{2} \left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c} { e^{- i \theta _2} } &{} { e^{- i \theta _3} } &{} 1 &{} { e^{- i \theta _1} } \\ { e^{- i \theta _2} } &{} { -e^{- i \theta _3}} &{} 1 &{} { -e^{- i \theta _1} } \\ { -e^{- i \theta _2}} &{} { e^{- i \theta _3} } &{} 1 &{} { -e^{- i \theta _1} } \\ { -e^{- i \theta _2}} &{} { -e^{- i \theta _3}} &{} 1 &{} { e^{- i \theta _1} } \end{array}\right) ,\quad V_3=\frac{1}{2} \left( \begin{array}{c@{\quad }c@{\quad }c@{\quad }c} { e^{- i \theta _3} } &{} { e^{- i \theta _2} } &{} { e^{- i \theta _1} } &{} 1 \\ { -e^{- i \theta _3}} &{} { e^{- i \theta _2} } &{} { -e^{- i \theta _1} } &{} 1 \\ { e^{- i \theta _3} } &{} { -e^{- i \theta _2} } &{} { -e^{- i \theta _1} } &{} 1 \\ { -e^{- i \theta _3}} &{} { -e^{- i \theta _2} } &{} { e^{- i \theta _1} } &{} 1 \end{array}\right) . \end{aligned} \end{aligned}$$
(31)

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Wang, MM., Qu, ZG., Wang, W. et al. Effect of noise on deterministic joint remote preparation of an arbitrary two-qubit state. Quantum Inf Process 16, 140 (2017). https://doi.org/10.1007/s11128-017-1594-y

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