Entanglement, Nonlocality, Quantum Teleportation of Two-mode Non-Gaussian States with Multiphoton Quantum Catalysis

Quantum-optical catalysis is a quantum state engineering that can convert states (Gaussian and/or non-Gaussian) into non-Gaussian states without changing the number of photons in the original states. This technique has been applied on many two-mode Gaussian states. In this paper, we introduce new two-mode non-Gaussian entangled states, called multiphoton catalytic pair coherent states (MCPCSs), based on the study of operating multiphoton quantum catalysis on two-mode non-Gaussian states, which are the pair coherent states (PCSs). By investigating linear entropy, Einstein-Podolsky-Rosen (EPR) correlation and EPR steering, it is shown that these properties in the new states can be enhanced compared with the PCSs by increasing the coherent parameter amplitude |ξ|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lvert \boldsymbol \xi \rvert $\end{document}. In the small regions of |ξ|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lvert \boldsymbol \xi \rvert $\end{document} and in the transmission coefficients space (t1,t2), the enhanced regions of the degree of entanglement are enlarged with increasing the numbers of catalytic photons, whereas in contrast to the EPR correlation and the EPR steering. Using the MCPCSs as entanglement resources to teleport a coherent state via the Braunstein and Kimble protocol, we calculate the average fidelity Fav of the teleportation process. The investigated results show that the average fidelity is enhanced in the large regions of the transmission coefficients t1,t2 as small values of |ξ|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lvert \boldsymbol \xi \rvert $\end{document}. In particular, for zero-photon catalysis, Fav is improved in the case of |ξ|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lvert \boldsymbol \xi \rvert $\end{document} high.