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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.06488 |
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| _version_ | 1866917353125576704 |
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| author | Fayad, Ammar |
| author_facet | Fayad, Ammar |
| contents | Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of continuous-variable decoherence, we prove that the unrestricted instantaneous reverse optimum exhibits a noiseless-to-noisy transition: below a critical squeezing-to-thermal ratio, reversal can be noiseless; above it, complete positivity forces irreducible reverse noise whose minimum cost we determine in closed form. The optimal reverse diffusion is uniquely covariance-aligned and simultaneously minimizes the geometric, metrological, and thermodynamic price of reversal. For multimode trajectories, the exact cost is additive in a canonical set of mode-resolved data, and a globally continuous protocol attains this optimum on every mixed-state interval. If a pure nonclassical endpoint is included, the same pointwise law holds for every $t>0$, but the optimum diverges as $2/t$: exact Gaussian reversal of a pure quantum state is dynamically unattainable. These results establish the exact Gaussian benchmark against which any broader theory of quantum reverse diffusion must be measured. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Score Reversal Is Not Free for Quantum Diffusion Models Fayad, Ammar Quantum Physics Machine Learning Mathematical Physics Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of continuous-variable decoherence, we prove that the unrestricted instantaneous reverse optimum exhibits a noiseless-to-noisy transition: below a critical squeezing-to-thermal ratio, reversal can be noiseless; above it, complete positivity forces irreducible reverse noise whose minimum cost we determine in closed form. The optimal reverse diffusion is uniquely covariance-aligned and simultaneously minimizes the geometric, metrological, and thermodynamic price of reversal. For multimode trajectories, the exact cost is additive in a canonical set of mode-resolved data, and a globally continuous protocol attains this optimum on every mixed-state interval. If a pure nonclassical endpoint is included, the same pointwise law holds for every $t>0$, but the optimum diverges as $2/t$: exact Gaussian reversal of a pure quantum state is dynamically unattainable. These results establish the exact Gaussian benchmark against which any broader theory of quantum reverse diffusion must be measured. |
| title | Score Reversal Is Not Free for Quantum Diffusion Models |
| topic | Quantum Physics Machine Learning Mathematical Physics |
| url | https://arxiv.org/abs/2603.06488 |