Assume 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-free. 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 bit is tested?
(ii) How many bits must you test for eavesdropping to be sure within a probability of 0.999 (1 - 1 thousandth) that the adversary wasn't listening?
(iii) How many bits must you test for eavesdropping to be sure within a probability of 0.999999 (1 - 1 millionth) that the adversary wasn't listening?