Quantum Channels as Temporal Correlations in Quantum Mechanics

Since the seminal work of J. S. Bell, spatial correlations in quantum mechanics have gained much progress. Nevertheless, up to now, the nature of temporal correlations remains unclear. In this work, based on the entangled-history theory, we prove rigorously that the temporal correlations can be just characterized by quantum channels, which are uniquely determined by state tomography technology. Moreover, the temporal correlations can be quantified in terms of the entanglement of formation. Examples are illustrated for the temporal correlation is either the strongest or the weakest.