We present a theory of entanglement transformations of Gaussian pure states
with local Gaussian operations and classical communication. This is the
experimentally accessible set of operations that can be realized with optical
elements such as beam splitters, phase shifts and squeezers, together with
homodyne measurements. We provide a simple necessary and sufficient condition
for the possibility to transform a pure bipartite Gaussian state into another
one. We contrast our criterion with what is possible if general local
operations are available.Comment: 12 pages, 1 figur