Continuous variable polarization entanglement in microwave domain

As a widely utilized information carrier, polarization microwave shows plenty of merits. Quantum microwave is booming gradually due to the development of superconducting technology, which makes it a promising potential to apply quantum entanglement to polarization microwave. In this paper, we introduce the concept of continuous variable polarization entanglement. Meanwhile, a scheme of polarization entanglement in microwave domain is proposed and simulated. The detail derivations are given and discussed. Polarization entangled microwaves are prepared by combining quadrature entangled signals and strong coherent signals on polarization beam splitters, and quadrature entangled signals are prepared by utilizing Josephson mixer. In order to probe the polarization entanglement between output signals, inseparability of Stokes vectors \begin{document}$I({\hat S_1},{\hat S_2})$\end{document}and \begin{document}$I({\hat S_2},{\hat S_3})$\end{document}, is analyzed in 100 MHz operation bandwidth of Josephson mixer. The relation between inseparability I and squeezing degree r and between inseparability I and amplitude ratio Q are analyzed respectively. The results show that \begin{document}$I({\hat S_1},{\hat S_2})$\end{document}is sensitive to the variation of Q , while \begin{document}$I({\hat S_2},{\hat S_3})$\end{document}is sensitive to the change of r . The physical reasons for these results are explored and discussed. Apart from these, \begin{document}$I({\hat S_1},{\hat S_2})$\end{document}remains its value above 1 under the condition in this paper, but on the contrary, \begin{document}$I({\hat S_2},{\hat S_3})$\end{document}keeps its value well below 1. It proves that \begin{document}${\hat S_2}$\end{document}and \begin{document}${\hat S_3}$\end{document}of Stokes vectors are inseparable from each other, thus output signals \begin{document}${\hat E_a}$\end{document}and \begin{document}${\hat E_b}$\end{document}of our scheme exhibit bipartite entanglement. The best entanglement appears nearly at about 70 MHz, at this point the minimum \begin{document}$I({\hat S_2},{\hat S_3})$\end{document}value is 0.25.