Interference and distinguishability in quantum mechanics

Abstract

Quantitative measures are introduced for the indistinguishability U of two quantum states in a given measurement, and the amount of interference I observable in this measurement. It is shown that these notions obey an inequality $\text{U ≧ I}$, which can be seen as an exact formulation of Bohr's claim that one cannot distinguish between two possible paths of a particle while maintaining an interference phenomenon. This formulation is applied to a neutron interferometer experiment of Badurek et al. It is shown that the formulation is stronger than an argument based on an uncertainty relation for phase and photon number as considered by these authors.