Electron interference and entanglement in coupled 1D systems with noise

We estimate the role of noise in the formation of entanglement and in the appearance of single- and two-electron interference in systems of coupled one-dimensional channels. Two cases are considered: a single-particle interferometer and a two-particle interferometer exploiting Coulomb interaction. In both of them, environmental noise yields a randomization of the carrier phases. Our results assess how the complementarity relation linking single-particle behavior to nonlocal quantities (such as entanglement and environment-induced decoherence) acts in electron interferometry. We show that in an experimental implementation of the setups examined, one- and two-electron detection probability at the output drains can be used to evaluate the decoherence and the degree of entanglement.