  The Hilbert space formalism of quantum theory manifests a map between
bipartite states and time evolutions, known as Jamiolkowski isomorphism. We
extend this map in a physical setting to prove the equality of spatial
correlations in bipartite systems and temporal correlations in local systems.
We show that these correlations can be observed using weak measurements. This
result has several practical and conceptual implications such as manifestation
of state independent decoherence, the correspondence between Bell and
Leggett-Garg inequalities, multipartite systems, the statistical properties of
evolutions in large systems, and computational gain, in evaluation of spatial
correlations in large systems.
