  A beam splitter is a basic linear optical element appearing in many optics
experiments and is frequently used as a continuous-variable entangler
transforming a pair of input modes from a separable Gaussian state into an
entangled state. However, a beam splitter is a passive operation that can
create entanglement from Gaussian states only under certain conditions. One
such condition is that the input light is squeezed. We demonstrate
experimentally that a beam splitter can create entanglement even from modes
which do not possess such a squeezing provided that they are correlated to but
not entangled with a third mode. Specifically, we show that a beam splitter can
create three-mode entanglement by acting on two modes of a three-mode fully
separable Gaussian state without entangling the two modes themselves. This beam
splitter property is a key mechanism behind the performance of the protocol for
entanglement distribution by separable states. Moreover, the property also
finds application in collaborative quantum dense coding in which decoding of
transmitted information is assisted by interference with a mode of the
collaborating party.
