We show the connection between a witness that detects dynamical maps with
initial system-environment correlations and a witness that detects
non-Markovian open quantum systems. Our analysis is based on studying the role
that state preparation plays in witnessing violations of contractivity of open
quantum system dynamics. Contractivity is a property of some quantum processes
where the trace distance of density matrices decrease with time. From this, we
show how a witness of initial-correlations is an upper bound to a witness of
non-Markovianity. We discuss how this relationship shows further connections
between initial system-environment correlations and non-Markovianity at an
instance of time in open quantum systems.Comment: 5 page
