The reference system and not completely positive open quantum dynamics. (arXiv:1702.08718v2 [quant-ph] UPDATED)

Open quantum dynamics in a tripartite scenario including a system, its
environment and a passive reference is shown to resolve several open questions
regarding not completely positive (NCP) dynamical maps as valid descriptions of
open quantum evolution. The steering states of the system and the environment
with respect to the reference, reduced down to a dense, compact set of states
of the system alone, provides a well defined domain of action for a bonafide
dynamical map describing the open evolution of the system. The map is not
restricted to being completely positive (CP) but it preserves the positivity of
all states in its domain. NCP open dynamics corresponding to different initial
configurations of the tripartite system are explored.

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