scenario where Alice and Bob are using the BB84 quantum key dis- tribution proto
ID: 3281373 • Letter: S
Question
scenario where Alice and Bob are using the BB84 quantum key dis- tribution protocol that was described in class. Alice sends 5 qubits to Bob. Bob measures in 4. Consider the following the following bases (in this order): zZ X Z X. The elements of his key are 01100. Alice tells Bob that he measured the first, second, and fifth qubits in the "correct" basis. (a) Based on the above information (and assuming there was no eavesdropper), what is the state of the first, second, and fifth qubits that Alice sent? (b) Is it possible to determine the states of the third and fourth qubits Alice sent? If so, what are the states of each qubit? If not, what are the possible states for the third and fourth qubits? Alice and Bob decide to compare all 5 bits of their key to determine if Eve was intercepting (They recognize that this will leave them with no key.) They find that they do not agree on the last bit of the key (c) What basis must Eve have measured the fifth qubit in? (d) Based on this new information, what is the state of the fifth qubit that Alice sent?Explanation / Answer
In BB84 protocols, if the measurement basis is correct then Bob measures the qubits exactly in the state that alice sent. The state for first second and fifth is
"010".
b) It is not possible, as the measurement of Bob disturbs the state. As the Bob measured the state in wrong basis so it has equal probabilities for 0 and 1 in other basis.
c) As the Alice mentioned that Bob is using the same basis what Alice has used and found that the key is not matching. So We can confirm that Eve has inturrpted the key and Eve has to be measured in the same basis. The answer is basis X.
d) The possiblities for any qubit is either 0 or 1. Alice has confirmed that 0 is not correct option so the correct state alice sent is 1.
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