Consider the quantum key establishment protocol. Assume that bit values, emitter basis, and receiver lter orientation are selected independently and uniformly at random (i.e., 50% chance for each of the bit values/ bases/orientations).
1)What is the joint entropy of the emitter bit value and receiver bit value?
My assumption is: H(X=0,Y=0) = 3/4 H(X=0,Y=1) = 1/4 H(X=1,Y=0) = 1/4 H(X=1,Y=1) = 3/4
H(Y=0,X=0) = 3/4 H(Y=0,X=0) = 1/4 H(Y=0,X=0) = 1/4 H(Y=0,X=0) = 3/4
I could not go further here.
2)What is the mutual information between the emitter bit value and the receiver bit value?
In my opinion, the filters can measure the polarasation of a photon if the filter and the photon do not agree the outcome is uniformly random. So, with respect to receiver bit value and emitter bit value we can find the sifted key.
Note:It is not a homework question.