Neither Quirrell nor Harry had any idea about the sheer genius of this final trap.
A few months before the current events, Albus Dumbledore had set up a Fidelius charm in a corner of the room and placed the stone in it. He then set up a complex switching charm based on two conditions.
1 - The absence of any and all dark magic traces on the person's core
2 - The absence of any intention of using the stone for their own gain.
The charm was then connected to the mirror to help detect the person's intentions.
Should the person want to use the stone, the switching charm wouldn't activate and they wouldn't get it. Should they use a hostage they had kidnapped, the mirror would simply show them their desire to go back home. Should they destroy the mirror, they would fail. The mirror was indestructible.
Absolute Protection.
Then, he had layered the mirror with some nastily powerful wards as a diversion. The sheer simplicity and brilliance of the trap was truly something else.
Had Harry not thought many times in his free afternoons of how he could heal people and enhance his healing skill by using the stone, Quirrell would have found the stone in Harry's pocket, since he wasn't a hostage, but had come to protect the stone.
But he had thought of it, and so the stone was beyond the reach of either of them.