  Vaidman has proposed a controversial criterion for determining the past of a
single quantum particle based on the "weak trace" it leaves. We here consider
more general examples of entangled systems and analyze the past of single, as
well as pairs of entangled pre- and postselected particles. Systems with
non-trivial time evolution are also analyzed. We argue that in these cases,
examining only the single-particle weak trace provides information which is
insufficient for understanding the system as a whole. We therefore suggest to
examine, alongside with the past of single particles, also the past of pairs,
triplets and eventually the entire system, including higher-order, multipartite
traces in the analysis. This resonates with a recently proposed top-down
approach by Aharonov, Cohen and Tollaksen for understanding the structure of
correlations in pre- and postselected systems.
