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Journal of Mathematical Physics

Some characterizations of quantum channel in infinite Hilbert spaces

Xiu-Hong Sun, Yuan Li

Published May 1, 2014• 3 citations
Publisher

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.

DOI
10.1063/1.4878264

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We first show that for any quantum states ρ on \documentclass[12pt]{minimal}\begin{document}H\mathcal {H}H\end{document}H and σ on \documentclass[12pt]{minimal}\begin{document}K\mathcal {K}K\end{document}K there exists a quantum channel Φ such that Φ(ρ) = σ, where \documentclass[12pt]{minimal}\begin{document}H\mathcal {H}H\end{document}H and \documentclass[12pt]{minimal}\begin{document}K\mathcal {K}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}Φ(IH)\Phi (I_{\mathcal {H}})Φ(IH​)\end{document}Φ(IH) exists or \documentclass[12pt]{minimal}\begin{document}Φ(IH)=IK.\Phi (I_{\mathcal {H}})=I_{\mathcal {K}}.Φ(IH​)=IK​.\end{document}Φ(IH)=IK.