Characterizations of fixed points of quantum operations
Yuan Li · Journal of Mathematical Physics · 2011
Let \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}}$\end{document}φA be a general quantum operation. An operator B is said to be a fixed point of \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}},$\end{document}φA, if \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}}(B)=B.$\end{document}φA(B)=B. In this note, we shall show conditions under which B, a fixed point \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}},$\end{document}φA, implies that B is compatible with the operation element of \documentclass[12pt]{minimal}\begin{document}$\phi _{\mathcal {A}}.$\end{document}φA. In particular, we offer an extension of the generalized Lüders theorem.