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Work statistics and quantum trajectories: No-click limit and non-Hermitian Hamiltonians

Manali Malakar and Alessandro Silva

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Phys. Rev. B 113, 064304 – Published 17 February, 2026

DOI: https://doi.org/10.1103/2nqj-dvqk

Abstract

We investigate quantum work statistics within the standard two-point measurement scheme in continuously monitored quantum systems, including the effects of generalized unitary evolution, possibly controlled by quantum circuit models, and multiple generalized measurements as well as postselection of no-click trajectories. We derive an explicit expression for the work generating function that naturally incorporates non-Hermitian dynamics arising from quantum jump processes and reveals deviations from the standard Jarzynski equality due to measurement-induced asymmetries. We illustrate our theoretical framework by analyzing a one-dimensional transverse-field Ising model under local spin monitoring. In this model, increased measurement strength projects the system onto the no-click state, leading to a suppression of energy fluctuations and measurement-induced energy saturation, reminiscent of the quantum Zeno effect. Moreover, we find signatures of the measurement-induced transition observed in the no-click limit in the moments of the work distribution.

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Phys. Rev. B 113, 064304– Published 17 February, 2026
  • Received 5 May 2025
  • Revised 7 January 2026
  • Accepted 12 January 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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