Duality Relations and Four-Particle Entanglement in Superconductor–Normal Conductor Setups

In normal–superconductor setups, it is widely known that entanglement can be generated through the process of Andreev reflection between two normal leads being coupled to a quantum dot. While this process is known well and its measurement via noise and similar characteristics has been performed in the past, the presence of interactions on the quantum dot may also give rise to the far less known process of four-particle entanglement. In this paper, we derive the general full charge transfer statistics formula for such devices in the presence of interactions and identify ways to measure the four-particle entanglement.