  In gauge theories and gravity, field variables are generally not
gauge-invariant observables, but such observables may be constructed by
"dressing" these or more general operators. Dressed operators create particles,
together with their gauge or gravitational fields which typically extend to
infinity. This raises an important question of how well quantum information can
be localized; one version of this is the question of whether soft charges fully
characterize a given localized charge or matter distribution. This paper finds
expressions for the non-trivial soft charges of such dressed operators.
However, a large amount of flexibility in the dressing indicates that the soft
charges, and other asymptotic observables, are not inherently correlated with
details of the charge or matter distribution. Instead, these asymptotic
observables can be changed by adding a general radiative (source-free) field
configuration to the original one. A dressing can be chosen, perturbatively, so
that the asymptotic observables are independent of details of the distribution,
besides its total electric or Poincar\'e charges. This provides an approach to
describing localization of information in gauge theories or gravity, and thus
subsystems, that avoids problems associated with nonlocality of operator
subalgebras. Specifically, this construction suggests the notions of
electromagnetic or gravitational splittings, which involve networks of Hilbert
space embeddings in which the charges play an important role.
