Double-direction quantum cyclic controlled remote state preparation of two-qubit states

In this article, we propose a four-party double-direction quantum cyclic controlled remote state preparation scheme, where two-qubit states can be remotely prepared cyclically among three correspondents both in clockwise and counterclockwise directions simultaneously under the control of the supervisor. Before presenting our four-party scheme, we give the quantum circuit diagram for constructing the 25-qubit quantum entangled channel. In our scheme, each correspondent merely carries out a four-qubit projective measurement and the supervisor only need to perform a single-qubit measurement in the Z-basis. After obtaining the measurement results from the other two correspondents and the supervisor, each correspondent can restore the desired states perfectly by applying proper unitary operations. The proposed four-party scheme can also be extended to the case containing m(m>3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m(m>3)$$\end{document} correspondents, by using a (8m+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(8m+1)$$\end{document}-qubit entangled channel. Discussions show that the success probability of both the proposed four-party and (m+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(m+1)$$\end{document}-party schemes can reach 1. We also analyze the control power of the supervisor in our scheme. Detailed analysis demonstrates that the control power of the supervisor can also be guaranteed.