Assume that you have an adversary that may or may not be trying to listen to your quantum channel as you attempt a quantum key exchange. Assume the channel is error free and noise fee. The adversary will either listen to every bit being transmitted or to none of the bits being transmitted.
(i) If an adversary listens to a single bit, what is the probability of catching it if the nit is tested?
(ii) How many bits must you test for eavesdropping to be sure within a probability of .999 (1-1 thousandth) that the adversary wasn't listning?
(iii) How many bits must you test for eavesdropping to be sure within a probability of .999999 (1-1 millionts) that the adversary wasn't listning?