Deterministic Controlled Remote State Preparation of Real-Parameter Multi-Qubit States via Maximal Slice States

Kaihang Zhou; Lei Shi; Bingbing Luo; Yang Xue; Chao Huang; Zhiqiang Ma; Jiahua Wei

doi:10.1007/s10773-019-04274-6

International Journal of Theoretical Physics

December 2019, Volume 58, Issue 12, pp 4079–4092 | Cite as

Deterministic Controlled Remote State Preparation of Real-Parameter Multi-Qubit States via Maximal Slice States

Authors
Authors and affiliations

Kaihang Zhou
Lei Shi
Bingbing Luo
Yang Xue
Chao Huang
Zhiqiang Ma
Jiahua Wei

Article

First Online: 15 October 2019

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Abstract

By exploiting three-qubit entangled states and appropriate measurement basis, we propose efficient protocols for deterministic controlled remote state preparation of arbitrary real-parameter multi-qubit states, in which the maximal slice states are used as quantum channel. The successful probability of our schemes can reach up to 100% by using multi-qubit mutually orthogonal measurement basis without the introduction of auxiliary particles. Based on the implementation schemes for preparing arbitrary two- and three-qubit states with real parameters, we have derived the controlled remote state preparation protocols for arbitrary real-parameter multi-qubit states.

Keywords

Controlled remote state preparation Real-parameter multi-qubit states Maximal slice states Successful probability

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Notes

Acknowledgements

This work is supported by the Program for National Natural Science Foundation of China (Grant No. 61803382), Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2018JQ6020) and China Postdoctoral Science Foundation Funded Project (Project No. 2018M643869).

Appendix: A

In Step 2 of Section 3, we present the state of particles (B₁,C₁,B₂,C₂,B₃,C₃) when the measurement result of particles (A₁,A₂,A₃) is |Γ₁〉. For the sake of the completeness, the state of particles (B₁,C₁,B₂,C₂,B₃,C₃) in terms of other measurement results |Γ_k〉 (k = 0, 2, 3,⋯ , 7) are supplemented as follows

$$ \begin{array}{@{}rcl@{}} |\psi_{0}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{0}|\psi\rangle_{total} \\ &=&\sum\limits_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle \\ &&\otimes\left( a_{0}|000\rangle+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{1}|001\rangle+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{2}|010\rangle\right. \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{3}|011\rangle+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{4}|100\rangle \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{5}|101\rangle +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{6}|110\rangle \\ &&+\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{7}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

$$ \begin{array}{@{}rcl@{}} |\psi_{2}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{2}|\psi\rangle_{total} \\ &=&\sum\limits_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle \\ &&\otimes\left( a_{2}|000\rangle-(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{3}|001\rangle-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{0}|010\rangle\right. \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{1}|011\rangle+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{6}|100\rangle \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{7}|101\rangle -(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{4}|110\rangle \\ &&-\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{5}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

$$ \begin{array}{@{}rcl@{}} |\psi_{3}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{3}|\psi\rangle_{total} \\ &=&\sum\limits_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle \\ &&\otimes\left( a_{3}|000\rangle+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{2}|001\rangle-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{1}|010\rangle\right. \\ &&-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{0}|011\rangle+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{7}|100\rangle \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{6}|101\rangle +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{5}|110\rangle \\ &&-\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{4}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

$$ \begin{array}{@{}rcl@{}} |\psi_{4}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{4}|\psi\rangle_{total} \\ &=&\sum\limits_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle \\ &&\otimes\left( a_{4}|000\rangle-(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{5}|001\rangle-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{6}|010\rangle\right. \\ &&-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{7}|011\rangle-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{0}|100\rangle \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{1}|101\rangle +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{2}|110\rangle \\ &&+\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{3}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

$$ \begin{array}{@{}rcl@{}} |\psi_{5}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{5}|\psi\rangle_{total} \\ &=&\sum\limits_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle \\ &&\otimes\left( a_{5}|000\rangle+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{4}|001\rangle-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{7}|010\rangle\right. \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{6}|011\rangle-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{1}|100\rangle \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{0}|101\rangle -(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{3}|110\rangle \\ &&+\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{2}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

$$ \begin{array}{@{}rcl@{}} |\psi_{6}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{6}|\psi\rangle_{total} \\ &=&{\sum}_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle\\ &&\otimes\left( a_{6}|000\rangle+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{7}|001\rangle+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{4}|010\rangle\right. \\ &&-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{5}|011\rangle-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{2}|100\rangle \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{3}|101\rangle -(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{0}|110\rangle \\ &&-\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{1}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

$$ \begin{array}{@{}rcl@{}} |\psi_{7}\rangle_{B_{1}C_{1}B_{2}C_{2}B_{3}C_{3}}&=&\langle{\varGamma}_{7}|\psi\rangle_{total} \\ &=&{\sum}_{|m_{C_{i}}\rangle=|x^{\pm}_{i}\rangle_{C_{i}}}\left( \frac{1}{\sqrt{2}}\right)^{3}P_{x_{1}}P_{x_{2}}P_{x_{3}}\otimes|m_{C_{1}}\rangle\otimes|m_{C_{2}}\rangle\otimes|m_{C_{3}}\rangle \\ &&\otimes\left( a_{7}|000\rangle-(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{6}|001\rangle+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{5}|010\rangle\right. \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{4}|011\rangle-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}a_{3}|100\rangle \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{2}|101\rangle +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}a_{1}|110\rangle \\ &&-\left.(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}a_{0}|111\rangle\right)_{B_{1}B_{2}B_{3}} \end{array} $$

Appendix: B

When the measurement result of particles $(A_{1},A_{2},A_{3})$ is $|{\varGamma }_{1}\rangle $ in Step 3 of Section 3, we have presented the unitary transformation $U_{{\varGamma }_{1}}$ that Bob needs to perform. For the other measurement results $|{\varGamma }_{k}\rangle ~(k=0,2,3,\cdots ,7)$, the unitary transformations $U_{{\varGamma }_{k}}$ on particles $(B_{1},B_{2},B_{3})$ are expressed as follows

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{0}}&=&|001\rangle\langle000|+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|001\rangle\langle001|+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|010\rangle\langle010| \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|011\rangle\langle011|+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|100\rangle\langle100| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|101\rangle\langle101| +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|110\rangle\langle110| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|111\rangle\langle111| \end{array} $$

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{2}}&=&|010\rangle\langle000|-(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|011\rangle\langle001|-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|000\rangle\langle010| \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|001\rangle\langle011|+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|110\rangle\langle100| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|111\rangle\langle101| -(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|100\rangle\langle110| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|101\rangle\langle111| \end{array} $$

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{3}}&=&|011\rangle\langle000|+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|010\rangle\langle001|-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|001\rangle\langle010| \\ &&-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|000\rangle\langle011|+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|111\rangle\langle100| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|110\rangle\langle101| +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|101\rangle\langle110| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|100\rangle\langle111| \end{array} $$

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{4}}&=&|100\rangle\langle000|-(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|101\rangle\langle001|-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|110\rangle\langle010| \\ &&-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|111\rangle\langle011|-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|000\rangle\langle100| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|001\rangle\langle101| +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|010\rangle\langle110| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|011\rangle\langle111| \end{array} $$

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{5}}&=&|101\rangle\langle000|+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|100\rangle\langle001|-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|111\rangle\langle010| \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|110\rangle\langle011|-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|001\rangle\langle100| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|000\rangle\langle101| -(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|011\rangle\langle110| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|010\rangle\langle111| \end{array} $$

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{6}}&=&|110\rangle\langle000|+(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|111\rangle\langle001|+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|100\rangle\langle010| \\ &&-(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|101\rangle\langle011|-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|010\rangle\langle100| \\ &&+(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|011\rangle\langle101| -(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|000\rangle\langle110| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|001\rangle\langle111| \end{array} $$

$$ \begin{array}{@{}rcl@{}} U_{{\varGamma}_{7}}&=&|111\rangle\langle000|-(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|110\rangle\langle001|+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|101\rangle\langle010| \\ &&+(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|100\rangle\langle011|-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}|011\rangle\langle100| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|010\rangle\langle101| +(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}|001\rangle\langle110| \\ &&-(-1)^{\langle x_{1}^{-}|m_{C_{1}}\rangle}(-1)^{\langle x_{2}^{-}|m_{C_{2}}\rangle}(-1)^{\langle x_{3}^{-}|m_{C_{3}}\rangle}|000\rangle\langle111| \end{array} $$

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Kaihang Zhou
- 1
Email authorView author's OrcID profile
Lei Shi
- 1
Bingbing Luo
- 2
Yang Xue
- 1
Chao Huang
- 1
Zhiqiang Ma
- 1
Jiahua Wei
- 1

1.Information and Navigation CollegeAir Force Engineering UniversityXi’anPeople’s Republic of China
2.Equipment Management and UAV Engineering CollegeAir Force Engineering UniversityXi’anPeople’s Republic of China

Deterministic Controlled Remote State Preparation of Real-Parameter Multi-Qubit States via Maximal Slice States

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