How to install deadbolt into a thin door?
To my knowledge, you won't find any modern in-door deadbolts that can accommodate such a thin door.  Even if you padded the width of your door around the installation point to reach the minimum needed, drilling the hole for the deadbolt will essentially remove a notch from your original door (deadbolts are commonly 1" thick).  Your spacers will have to go all the way to the edge of the door to conceal the deadbolt.

A simpler solution would be to use a surface-mount deadbolt, which requires only that you drill a hole for the rim cylinder.  You may have to add a spacer around the rim cylinder to get a flush fit, but it won't end up being the only thing concealing the lock mechanism from tampering.  That link shows several types, including jimmy proof deadbolts and night latches.