I'm afraid that I can't fully agree with Nick L when he says:
"let me specfically state that it is impossible to get into vortex ring state while maneuvering around the hover and performing maneuvers like a quick stop. Why? Because vortex ring state requires rates of descent of approximately 800 feet per minute to 2000 feet per minute".
On my type we fly quickstops nb 50 ft agl, and of course you should never see a RoD anything close to the 800 to 2000 fpm figures to which Nick refers, even if the quickstop is grossly mis-mandled and a RoD is allowed to build up during the manouevre.
However, as I see it it is not just the physical RoD as you sink that should concern us. As you flare the aircraft into the quickstop the angle at which the forward airspeed passes over (and through) the disc now changes. Consider it as a velocity, and take its 2 components (horizontal and vertical relative to the disc) and you will see that the disc is now exposed to an apparent RoD airflow that can be very significant. This apparent RoD airflow, allied to a sink during a mis-handled quickstop, could indeed lead to problems.
(I have drawn a lovely picture but I can't work out how to import it!)
It would be an extreme case that approached vortex ring parameters, but the difficulty that Nick described with the zero airspeed condition when operating downwind would only push you closer to this extreme condition.
Does that make sense?