Fidelity of quantum interferometers

Abstract

For a generic interferometer, the conditional probability density distribution p(|m), for the phase given measurement outcome m will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as Δ ∼1/N (the standard limit), or Δ∼1/N (the Heisenberg limit). We propose an alternative measure of phase sensitivity-the fidelity of an interferometer-defined as the Shannon mutual information between the phase shift and the measurement outcomes m. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. For the case where there exists no a priori information on the phase shift, we find the surprising result that maximally entangled state input leads to a lower fidelity than Fock state input, for the same photon number. © 2006 U. S. Government.