Minimum assured fidelity and minimum average fidelity in quantum teleportation of single qubit using non-maximally entangled states

We study use of non-maximally entangled states (NME) in quantum teleportation (QT) of single qubit. We find that if NME states are written in the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${| E \rangle =\sum_{j,k} {E_{jk} | j \rangle | k \rangle}}$$\end{document} , where (j, k) = 0 and 1, and maximally entangled Bell-basis is used in measurement by the sender, the ‘Minimum Assured Fidelity’ (the minimum value of fidelity for all possible information states) for QT is 2C/(1 + C), where C is the concurrence of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${| E \rangle }$$\end{document} given by C = 2|det (E)| and E is the matrix defined by the coefficients Ejk. We also find the average of fidelity over various results of Bell-state measurement and its minimum value over all possible information states and discuss it for some special cases. We also show that, to evaluate quality of imperfect QT, minimum assured fidelity is a better measure than concurrence or minimum average fidelity.