We discuss the prospects of performing Heisenberg-limited quantum sensing and
metrology using a Mach-Zehnder interferometer with input states that are superpositions
of twin-Fock states and where photon number parity measurements are made on one of
the output beams of the interferometer. This study is motivated by the experimental
challenge of producing twin-Fock states on opposite sides of a beam splitter. We focus on
the use of the so-called pair coherent states for this purpose and discuss a possible
mechanism for generating them. We also discuss the prospect of using other superstitions
of twin-Fock states, for the purpose of interferometry.
We consider a quantum system of two nonorthogonal bipartite quantum
states. We distribute the qubits between two parties, Alice and Bob. They each measure their qubits and then compare their measurement results to determine which state they were sent. This procedure is error-free, which implies that it must sometimes fail. In addition, no quantum memory is required; it is not necessary for one of the qubits to be stored until the result of the measurement on the other is known. We consider the cases in which, should a failure occur, both parties receive a failure signal or only one does. In the latter case, if the two states share the same Schmidt basis, the states can be discriminated with the same failure probability as would be obtained if the qubits were measured together. This scheme is sufficiently simple that it can be generalized to multipartite qubit and qudit states. Applications to quantum secret sharing are discussed.