  A key feature of the many-body localized phase is the breaking of ergodicity
and consequently the emergence of local memory; revealed as the local
preservation of information over time. As memory is necessarily a time
dependent concept, it has been partially captured by a few extant studies of
dynamical quantities. However, these quantities are neither optimal, nor
democratic with respect to input state; and as such a fundamental and complete
information theoretic understanding of local memory in the context of many-body
localization remains elusive. We introduce the dynamical Holevo quantity as the
true quantifier of local memory, outlining its advantages over other quantities
such as the imbalance or entanglement entropy. We find clear scaling behavior
in its steady-state across the many-body localization transition, and determine
a family of two-parameter scaling ans\"atze which captures this behavior. We
perform a comprehensive finite size scaling analysis of this dynamical quantity
extracting the transition point and scaling exponents.
