title: Extracting information from a qubit by multiple observers: toward a theory of sequential state discrimination.
abstract: 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 Letter is a first step toward developing a theory of nondestructive sequential quantum measurements, which could be useful in quantum communication schemes.
authors.affiliation: Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
authors.forename: Janos
authors.initials: J
authors.lastname: Bergou
authors.affiliation: Department of Mathematics, Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016, USA.
authors.forename: Edgar
authors.initials: E
authors.lastname: Feldman
authors.affiliation: Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Hillery