Relating local time evolutions with bipartite states: An exact map manifested by weak measurements

We suggest a natural mapping between bipartite states and quantum evolutions of local states, which is a Jamiolkowski map. It is shown that spatial correlations of weak measurements in bi-partite systems precisely coincide with temporal correlations of local systems. This mapping has several practical and conceptual implications on the correspondence between Bell and Leggett-Garg inequalities, the statistical properties of evolutions in large systems, temporal decoherence and computational gain, in evaluation of spatial correlations of large systems. [Editor’s note: for a video of the talk given by Prof. Reznik at the Aharonov-80 conference in 2012 at Chapman University, see quantum.chapman.edu/talk-23.]