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    Information conservation relations for weak measurement and its reversal

    Yusef Maleki*, Luis D. Zambrano Palma†, and M. Suhail Zubairy‡

    • Institute for Quantum Science and Engineering, Texas A&M University, College Station, Texas 77843, USA

    • *Contact author: maleki@tamu.edu
    • †Contact author: ldzambra@tamu.edu
    • ‡Contact author: zubairy@tamu.edu

    Phys. Rev. A 113, 012215 – Published 12 January, 2026

    DOI: https://doi.org/10.1103/4h4b-3xss

    Abstract

    We investigate the information distribution among different entities in the weak-measurement 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.

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