  We study sequential state discrimination measurements performed on the same
qubit by subsequent observers. Specifically, we focus on the case when the
observers perform a kind of a minimum-error type state discriminating
measurement where the goal of the observers is to maximize their joint
probability of successfully guessing the state that the qubit was initially
prepared in. We call this the joint best guess strategy. In this scheme, 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, and so on to altogether N consecutive
receivers who all perform measurements on it. The goal for all observers is to
determine which state Alice sent. In the joint best guess strategy, every time
a system is received the observer is required to make a guess, aided by the
measurement, about its state. The price to pay for this requirement is that
errors must be permitted, the guess can be correct or in error. There is a
nonzero probability for all the receivers to successfully identify the
initially prepared state, and we maximize this joint probability of success.
This work is a step toward developing a theory of nondestructive sequential
quantum measurements and could be useful in multiparty quantum communication
schemes based on communicating with single qubits, particularly in schemes
employing continuous variable states. It also represents a case where
subsequent observers can probabilistically and optimally get around both the
collapse postulate and the no-broadcasting theorem.
