We show the connection between a witness that detects dynamical maps withinitial system-environment correlations and a witness that detectsnon-Markovian open quantum systems. Our analysis is based on studying the rolethat state preparation plays in witnessing violations of contractivity of openquantum system dynamics. Contractivity is a property of some quantum processeswhere the trace distance of density matrices decrease with time. From this, weshow how a witness of initial-correlations is an upper bound to a witness ofnon-Markovianity. We discuss how this relationship shows further connectionsbetween initial system-environment correlations and non-Markovianity at aninstance of time in open quantum systems.
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