Quantum and classical correlations of spatial and spin degrees of freedom in quantum rings

A one-dimensional mesoscopic ring with one input and two output leads acts as a spintronic beam splitter. The spatial degree of freedom, i.e., the presence of two different possible output channels, gets intertwined with the spin direction as a consequence of quantum interference and spin-orbit interaction. We investigate this kind of spatial-spin correlation, and show that the output density operator contains no quantum entanglement in the important special case when the device polarizes a perfectly random input spin state. However, the correlations are in general not purely classical, we also present specific input states with maximal spatial-spin entanglement after the ring.