  We introduce the entanglement gauge describing the combined effects of local
operations and nonlocal unitary transformations on bipartite quantum systems.
The entanglement gauge exploits the invariance of nonlocal properties for
bipartite systems under local (gauge) transformations. This new formalism
yields observable effects arising from the gauge geometry of the bipartite
system. In particular, we propose a non-Abelian gauge theory realized via two
separated spatial modes of the quantized electromagnetic field manipulated by
linear optics. In this linear optical realization, a bi-partite state of two
separated spatial modes can acquire a non-Abelian geometric phase.
