Nonclassical mixed states that generate zero entanglement with a beam splitter

Abstract

Beam splitters are routinely used for generating entanglement. Their entangling properties have been studied extensively, with nonclassicality of the input states a prerequisite for entanglement at the output. Here we quantify the amount of entanglement generated by weakly-reflecting beam splitters, and look for nonclassical states that are not entangled by general beam splitters. We extend the known class of results to mixed and non-Gaussian states, finding that inputting highly nonclassical combinations of unpolarized states that are squeezed and displaced onto a beam splitter can still yield separable output states. This is important in light of the challenge of characterizing mixed state entanglement. We further identify a parallel between SU(2) unpolarized states and the two-mode vacuum. Our result is crucial for understanding the generation of modal entanglement by beam splitters.