Quantum elimination measurements

Abstract

If an initial state is prepared from a known set, then the aim of a quantum state elimination measurement is to rule out a subset of the possible initial states. We use semi-definite programming to find either bounds or exact results on the success probabilities of certain elimination measurements. In conjunction we use an analytic approach to find optimal measurements. We obtain optimal measurements for unambiguous elimination in a two-qubit case where each qubit is in one of two possible states. We also show how it might be possible to use our elimination measurements in a QKD protocol. In addition we prove that the best method to eliminate the highest average number of states for sequences of qubits with each qubit in one of two possible states is individual unambiguous measurements. Furthermore we show the method of decomposing a unitary matrix into beamsplitter-like operations found by Reck et al. and apply this to our elimination measurement to realise a way of experimental implementation. In the final chapter we look at joint measurements and find the optimal probe state that we would use to minimise the uncertainty in our estimation of the sharpness of a measurement between two observables.