Generating quantum ensembles via reverse-time quantum diffusions

• URL: http://arxiv.org/abs/2606.03848v1
• Date: Tue, 02 Jun 2026 16:27:04 GMT
• Title: Generating quantum ensembles via reverse-time quantum diffusions
• Abstract summary: We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems.<n>We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise.<n>This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schrödinger equation of a forward noising dynamics, we derive the exact reverse-time dynamics for quantum trajectories, whose law coincides with the time-reversal of the original process. We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise but a state-dependent feedback Hamiltonian, a direct analogue of the "score function" of generative classical diffusion models. This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states. We show how the denoising dynamics can be directly learnt from forward trajectory data, and how to exploit purification to initialise the denoising process.

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