Characterize the set of possible true states under unknown bath–environment interactions

Determine the set of possible true quantum states for an open quantum system conditioned, in part, on naturally occurring measurements of the unobserved baths, given that the types of interactions between the unobserved baths and the larger environment acting as a measurement apparatus are generally unknown. Specifically, characterize this set in general for systems where only a single observer monitors part of the environment and the remaining bath interactions are inaccessible or unspecified.

Background

The paper defines the “true” state ρ_T(t) of a quantum system as the state conditioned on measurements on all baths extending far into the past, ideally yielding a pure trajectory governed by a stochastic Schrödinger equation. In realistic scenarios, only part of the environment is observed, while other baths remain unmeasured, and their outputs may be indirectly measured by the larger environment acting as a measurement apparatus.

The authors note that the set of possible true states depends on the specific interactions between the unobserved baths and the environment, which are generally unspecified and thus not known. While they identify a unique and natural unravelling (heterodyne detection) for their optomechanical system under criteria of invariance and Markovianity, they emphasize that, in general, the full set of possible true states is not characterized due to unknown bath–environment interactions.