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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.24587 |
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Table of Contents:
- Gentle measurements of quantum states do not entirely collapse the initial state. Instead, they provide a post-measurement state at a prescribed trace distance $α$ from the initial state together with a random variable used for quantum learning of the initial state. We introduce here the class of $α-$locally-gentle measurements ($α-$LGM) on a finite dimensional quantum system which are product measurements on product states and prove a strong quantum Data-Processing Inequality (qDPI) on this class using an improved relation between gentleness and quantum differential privacy. We further show a gentle quantum Neyman-Pearson lemma which implies that our qDPI is asymptotically optimal (for small $α$). This inequality is employed to show that the necessary number of quantum states for prescribed accuracy $ε$ is of order $1/(ε^2 α^2)$ for both quantum tomography and quantum state certification. Finally, we propose an $α-$LGM called quantum Label Switch that attains these bounds. It is a general implementable method to turn any two-outcome measurement into an $α-$LGM.