Question: 2. /25 Alice and Bob are using BB-84 to establish a secret key. Eve knows that if she measures in a random basis it will

 2. /25 Alice and Bob are using BB-84 to establish a

2. /25 Alice and Bob are using BB-84 to establish a secret key. Eve knows that if she measures in a random basis it will disturb Alice's transmissions and cause errors in Bob's copy of the secret key. Then Alice and Bob will notice her eavesdropping. So, she will be sneaky. With probability 1 p, Eve will not measure Alice's signal at all, but with probability p she will measure randomly in either {[0),(1)} or {I+), 1}}. Consider a case when Alice transmits in the same basis that Bob measures in. Given the attack by Eve, calculate as a function of p the probability that Bob's measurement outcome (i.e., his key bit) is equal to the bit transmitted by Alice. 2. /25 Alice and Bob are using BB-84 to establish a secret key. Eve knows that if she measures in a random basis it will disturb Alice's transmissions and cause errors in Bob's copy of the secret key. Then Alice and Bob will notice her eavesdropping. So, she will be sneaky. With probability 1 p, Eve will not measure Alice's signal at all, but with probability p she will measure randomly in either {[0),(1)} or {I+), 1}}. Consider a case when Alice transmits in the same basis that Bob measures in. Given the attack by Eve, calculate as a function of p the probability that Bob's measurement outcome (i.e., his key bit) is equal to the bit transmitted by Alice

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