Maximum Fidelity Retransmission of Mirror Symmetric Qubit States

Abstract

In this paper we address the problem of optimal reconstruction of a quantum state from the result of a single measurement when the original quantum state is known to be a member of some specified set. A suitable figure of merit for this process is the fidelity, which is the probability that the state we construct on the basis of the measurement result is found by a subsequent test to match the original state. We consider the maximisation of the fidelity for a set of three mirror symmetric qubit states. In contrast to previous examples, we find that the strategy which minimises the probability of erroneously identifying the state does not generally maximise the fidelity.