Accurate Modeling of Reduced-State Dynamics

TL;DR

This paper explores how to accurately model reduced-state dynamics considering system-environment interactions, especially when initial correlations or known features challenge standard modeling assumptions, providing complete characterizations and certification methods.

Contribution

It introduces a comprehensive analysis of reduced dynamics with initial correlations, characterizes unitaries for qubits that admit consistent models, and proposes methods to certify initial correlations from system observations.

Findings

Restrictions on reduced dynamics can emerge from known interaction features.

Complete characterization of unitaries for qubits that allow consistent reduced models.

Initial correlations can be certified through system evolution observations.

Abstract

In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the system-environment interaction. When the experimenter takes into account certain known features of the interaction such as its invariant subspaces or its non-local content, it may not be possible to consistently model the system evolution over a certain time interval using a standard Stinespring dilation, which assumes the system and environment to be initially uncorrelated. Simple examples demonstrating how restrictions can emerge are presented below. When the system and environment are qubits, we completely characterize the set of unitaries that always generate reduced dynamics capable of being modeled using a consistent Stinespring dilation. Finally, we show how any initial correlations between the system and environment can be certified by observing the system transformation alone during certain joint evolutions.