Tiled Map with libGDX

im developing a platformer game, with libGDX, im thinking of using Tiled Map as level editor. I have a concern about the graphics, if my graphics will be done as png format, is it possible to draw the levels with tiled map without the losing any quality if my game will be run on IOS Android and Desktop.
To make it clear : what is the tile size that will not lose quality with different screen sizes?

I would not expect any loss of quality anywhere, but this is really a question you should try asking in the libGDX community.