  We discuss sequential unambiguous state-discrimination measurements performed
on the same qubit. Alice prepares a qubit in one of two possible states. The
qubit is first sent to Bob, who measures it, and then on to Charlie, who also
measures it. The object in both cases is to determine which state Alice sent.
In an unambiguous state discrimination measurement, we never make a mistake,
i.e. misidentify the state, but the measurement may fail, in which case we gain
no information about which state was sent. We find that there is a nonzero
probability for both Bob and Charlie to identify the state, and we maximize
this probability. The probability that Charlie's measurement succeeds depends
on how much information about the state Alice sent is left in the qubit after
Bob's measurement, and this information can be quantified by the overlap
between the two possible states in which Bob's measurement leaves the qubit.
This paper is a first step toward developing a theory of nondestructive
sequential quantum measurements, which could be useful in quantum communication
schemes.
