Bending arrow between 2 nodes adds additional arrow when using anchors

Question

I want to do a bending arrow between two nodes of a TikZ picture, and using the border anchors (north, east, south...). Here is a MWE:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\node[draw] (n1) at (0,0) {};
\node[draw] (n2) at (1,0) {};
\draw[->] (n1.east) edge[bend left] (n2.west);
\end{tikzpicture}
\end{document}

Which yields:

But I want:

If I remove the bending (i.e. (n1.east) -- (n2.west)), or if I remove the anchor of the starting node (i.e. (n1) -- (n2.west)), or when I do a simple line and not an arrow (i.e. \draw[]) there is no unexpected behaviour, but when I have all of this at once, the additional arrow appears.

I want a solution that keeps the anchors, the arrow and the bending.

Thank you for your help.