Some characterizations of quantum channel in infinite Hilbert spaces

Abstract

We first show that for any quantum states ρ on \documentclass[12pt]{minimal}\begin{document}$\mathcal {H}$\end{document}H and σ on \documentclass[12pt]{minimal}\begin{document}$\mathcal {K}$\end{document}K there exists a quantum channel Φ such that Φ(ρ) = σ, where \documentclass[12pt]{minimal}\begin{document}$\mathcal {H}$\end{document}H and \documentclass[12pt]{minimal}\begin{document}$\mathcal {K}$\end{document}K are finite or infinite dimensional Hilbert spaces. Then we consider some conclusions for the quantum channel Φ such that Φ(ρ) = σ and \documentclass[12pt]{minimal}\begin{document}$\Phi (I_{\mathcal {H}})$\end{document}Φ(IH) exists or \documentclass[12pt]{minimal}\begin{document}$\Phi (I_{\mathcal {H}})=I_{\mathcal {K}}.$\end{document}Φ(IH)=IK.