Please follow the marking criteria, (NO AI NO Plagiarism) Please do all the calculations things with the formula. Include all the necessary screenshots)
1 With random bases and no eavesdropper, the key should be 100% correct since the potentially errored bits are all eliminated.
2 With random bases and an eavesdropper, some of the bits in the key will be wrong, because Eve will only get the correct bases 50% of the time. Of those qubits where her bases are wrong, 50% will be misread. Try drawing it out as a tree of possibilities. Writing down the expected numbers of qubits for each possibility. Once you have done this, you should be able to calculate the number of errors quite easily.
3 In the satellite QKD exercise, the satellite shares keys with both ground stations. However, the satellite is the only party that knows both these keys (which is why it needs to be trusted). Some people assumed that the satellite XORs the two keys together. This is quite correct, but what next? Hint: What if it sends the output of the XOR to one (or both) of the ground stations through a classical channel? How could this help share a key between the two ground stations?
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