From Quantum Computing: A Gentle Introduction:
In the BB84 protocol, how many bits do Alice and Bob need to compare to have a 90% chance of detecting Eve's presence?
I am having some trouble calculating this value. I understand that 50% of the time, Eve measures in the wrong basis and sends Bob a different bit than Alice sent, and after Alice and Bob compare their measuring bases, on average, Bob is left with 50% of his measured qubits. Therefore, given that Eve eavesdropped, there is a 25% probability that a given remaining bit is wrong. From this information, how would I calculate the number of bits needed to detect Eve with 90% confidence?