Purifying two-qubit entanglement in nonidentical decoherence by employing weak measurements

In this paper, we propose a feasible scheme for purifying two-qubit entanglement in the presence of decoherence by employing weak measurements. As long as the entanglement parameter α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} and the measurement strength p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} satisfy a certain condition, we can always achieve the purification without reference to the initial state. Furthermore, an arbitrary initial state can be directly purified into the maximally entangled state by setting measurement strength p=1-α1-α2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p=1-\frac{\left| \alpha \right| }{\sqrt{1-\left| \alpha \right| ^{2}}}$$\end{document}. The success probability of our scheme not only depends on measurement strength, but also closely links to the initial state.