How entangled pairs act as measuring rods on manifolds of generalized coherent states

Generalized coherent states arise from reference states by the action of locally compact transformation groups and thereby form manifolds on which there is an invariant measure. It is shown that this implies the existence of canonically associated Bell states that serve as measuring rods by relating the metric geometry of the manifold to the observed Einstein-Podolsky-Rosen (EPR) correlations. It is further shown that these correlations can be accounted for by a hidden variable theory which is nonlocal but invariant under the stability group of the reference state.