  We present a geometric approach to the characterization of separability and
entanglement in pure Gaussian states of an arbitrary number of modes. The
analysis is performed adapting to continuous variables a formalism based on
single subsystem unitary transformations that has been recently introduced to
characterize separability and entanglement in pure states of qubits and qutrits
[arXiv:0706.1561]. In analogy with the finite-dimensional case, we demonstrate
that the $1 \times M$ bipartite entanglement of a multimode pure Gaussian state
can be quantified by the minimum squared Euclidean distance between the state
itself and the set of states obtained by transforming it via suitable local
symplectic (unitary) operations. This minimum distance, corresponding to a,
uniquely determined, extremal local operation, defines a novel entanglement
monotone equivalent to the entropy of entanglement, and amenable to direct
experimental measurement with linear optical schemes.
