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  • Open Access

Stochastic Schrödinger equations for quantum reverse diffusion

Einar Gabbassov*

  • *Contact author: egabbass@uwaterloo.ca
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Phys. Rev. Research 8, 023329 – Published 23 June, 2026

DOI: https://doi.org/10.1103/f7fd-2rb9

Abstract

The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are analytical stochastic Schrödinger equations for quantum reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. We show that the reverse processes generalize the forward dynamics by combining the noise effects of the forward processes with an additional stochastic drift that dynamically steers a quantum state back to its initial configuration. Consequently, the exact reverse stochastic Schrödinger equations admit closed-form solutions that can be implemented in real time without the need for variational techniques. Our findings establish an analytical framework for quantum state recovery, noise-resilient quantum gates, quantum generative modeling, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.

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Phys. Rev. Research 8, 023329– Published 23 June, 2026
  • Received 30 November 2025
  • Accepted 1 June 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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