Information conservation relations for weak measurement and its reversal

TL;DR

This paper derives exact information conservation relations in weak quantum measurements, including reversal processes, offering a detailed understanding of information flow in monitored open quantum systems.

Contribution

It introduces a unified framework for outcome-resolved information relations in weak measurements and reversals, extending to finite photon counts and providing new insights into quantum information dynamics.

Findings

Exact information conservation relations for weak measurements.

Quantitative trade-offs linking information change and measurement outcomes.

Outcome-resolved analysis of information flow in open quantum systems.

Abstract

We investigate the information distribution among different entities in the weak measurements protocol. Focusing on multilevel, decaying systems under continuous (no-click) monitoring, we derive exact, conservation-type information relations that hold for each outcome in the record. Analogous relations hold when an explicit reversal is applied, with the reversal success probability entering the relation. We extend the framework to finite-count outcomes (arbitrary photon numbers) obtaining quantitative trade-offs that link information change in the weak measurement process to the entities to which the information is distributed. These results provide a unified, outcome-resolved account of information flow in monitored open quantum dynamics and provide insight into a deeper understanding of open-system dynamics and its control.