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  • Open Access

Equilibration of objective observables in a dynamical model of quantum measurements

Sophie Engineer1,2,*, Tom Rivlin3, Sabine Wollmann2, Mehul Malik2, and Maximilian P. E. Lock3,4,†

  • *Contact author: sophiengineer@gmail.com
  • †Contact author: maximilian.paul.lock@tuwien.ac.at
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Phys. Rev. A 113, 032205 – Published 9 March, 2026

DOI: https://doi.org/10.1103/lkqb-jdmg

Abstract

The challenge of understanding quantum measurement persists as a fundamental issue in modern physics. Particularly, the abrupt and energy-nonconserving collapse of the wave function appears to contradict classical thermodynamic laws. The contradiction can be resolved by considering measurement itself to be an entropy-increasing process, driven by the second law of thermodynamics. One such resolution explains the apparently irreversible emergence of objective outcomes in an isolated, unitarily evolving quantum system via the theory of closed-system equilibration. Working within this framework, we construct the set of “objectifying observables” that best encode the measurement statistics of a system in an objective manner and establish a measurement error bound to quantify the probability an observer will obtain an incorrect measurement outcome. Using this error bound, we show that the objectifying observables readily equilibrate on average under the set of Hamiltonians which preserve the outcome statistics on the measured system. Using a random matrix model for this set, we numerically determine the measurement error bound, finding that the error only approaches zero with increasing environment size when the environment is coarse grained into so-called observer systems. This indicates the necessity of coarse graining an environment for the emergence of objective, classical measurement outcomes.

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Phys. Rev. A 113, 032205– Published 9 March, 2026
  • Received 16 December 2024
  • Accepted 10 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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