Given a list of ciphertexts, how to identify the ones that used the same key for encryption
If you assume the keys are random yet the plain text are english. Xoring two cipher texts with different keys will look like random noise. Yet if you xor two messages with same key you get a complex distribution of pairs of English messages, very not random. A simple histogram should be sufficient to tell the distributions apart.
If the keys are not random(possibly leading to other attacks) you will probably still be able to pull off the same attack though you will need to study the histogram of xoring English messages so you can detect it. With random keys it won't even be necessary.