Key distribution via entanglement
I understand how keys are sent via quantum entanglement. So that Alice and Bob each receive one of the entangled bits, and upon measuring it, assuming they used the same basis will be certain of the others result. Then using this they can detect the presence of an eavesdropper.
My question is can this be used to distribute the same key to more than two people?
Which would essentially create a broadcasting type system. This would obviously be limited to exactly n users, so not complete broadcasting. It would require the entangled states to make all the bits the same i think, so if Alice reads a 0 everyone else using the same basis as her reads 0, and make the chance of all parties correctly choosing the correct basis 1/(2^n)?
Assuming it is possible, in a hypothetical 3 user system, would it allow the detection of an eavesdropper by using the measurements of two people who did use the same basis to check (but not the third)?
So the key would be bits 1,4,8,9. and there would be two users that could compare each of the other 6 bits for the presence of an eavesdropper?