Removing wine stains from a decanter
It's a bit of a blunt instrument, but I'd tend to just go straight for hydrogen peroxide if it's available where you are. It breaks up all sorts of organic dyes via oxidation, and it slowly decomposes by itself, especially in sunlight, so you can just rinse (thoroughly) and leave it to dry in the sun.

(NB: I have never owned a wine decanter, and take no responsibility if your decanter dissolves, explodes, or spontaneously gains the ability to sing operatically.)