Correlation preserving map between bipartite states and temporal evolutions

Understand

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.