Exchange of information between system and environment: facts and myths

TL;DR

This paper critically examines how information exchange between a system and its environment is characterized, challenging common assumptions and proposing a measure for information loss based on reduced dynamics.

Contribution

It clarifies misconceptions about trace distance and introduces a new measure for information loss in reduced dynamics, emphasizing asymmetry in system-environment interactions.

Findings

Trace distance does not reliably indicate information exchange.

A new measure of loss quantifies deviation from unitary dynamics.

Symmetry assumptions in information transfer are invalid.

Abstract

The exchange of "information" between a system and its environment based on the reduced dynamics is investigated. The association of trace distance with information cannot be stated, because of lack of symmetry between leakage from the system and absorbability by the environment. A measure of loss for the reduced dynamics is established, which may be seen as a deviation from exact unitary dynamics.