Extracting unambiguous information from a single qubit by sequential observers

In a recent paper [Phys. Rev. Lett. 111, 100501 (2013)], a scheme was proposed where subsequent observers can extract unambiguous information about the initial state of a qubit, with finite joint probability of success. Here, we generalize the problem for arbitrary preparation probabilities (arbitrary priors). We discuss two different schemes: one where only the joint probability of success is maximized and another where, in addition, the joint probability of failure is also minimized. We also derive the mutual information for these schemes and show that there are some parameter regions for the scheme without minimizing the joint failure probability where, even though the joint success probability is maximum, no information is actually transmitted by Alice.

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