# The reference system and not completely positive open quantum dynamics

## TL;DR

This paper introduces a tripartite reference system framework that clarifies the validity of not completely positive (NCP) quantum dynamical maps, showing they can be physically meaningful within a well-defined domain.

## Contribution

It provides a new tripartite reference-based approach to interpret NCP quantum dynamics as valid, expanding the understanding of open quantum system evolution.

## Key findings

- NCP maps can be valid within a specific domain of states.
- The tripartite framework clarifies the physical relevance of NCP dynamics.
- Different initial configurations lead to diverse NCP dynamics.

## Abstract

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.