NOON state measurement probabilities and outcome fidelities: a Bethe Ansatz approach

Abstract A recently proposed extended Bose-Hubbard model, one that is a quantum integrable model, provides a framework for a NOON state generation protocol. Here we derive a Bethe Ansatz solution for the model. The form of the solution provides the means to obtain exact asymptotic expressions for the energies and eigenstates. These results are used to derive formulae for measurement probabilities and outcome fidelities. We benchmark these results against numerical calculations.