  The characterizing feature of a many-body localized phase is the existence of
an extensive set of quasi-local conserved quantities with an exponentially
localized support. This structure endows the system with the signature
logarithmic in time entanglement growth between spatial partitions. This
feature differentiates the phase from Anderson localization, in a
non-interacting model. Experimentally measuring the entanglement between large
partitions of an interacting many-body system requires highly non-local
measurements which are currently beyond the reach of experimental technology.
In this work we demonstrate that the defining structure of many-body
localization can be detected by the dynamics of a simple quantity from quantum
information known as the total correlations which is connected to the local
entropies. Central to our finding is the necessity to propagate specific
initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics
of the local entropies and total correlations requires only local measurements
in space and therefore is potentially experimentally accessible in a range of
platforms.
