Approximate pushforward designs and image bounds on approximations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917116439953408 |
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| author | Czartowski, Jakub Sawicki, Adam Życzkowski, Karol |
| author_facet | Czartowski, Jakub Sawicki, Adam Życzkowski, Karol |
| contents | We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten $p$-norms and Lipschitz continuity arguments, we derive bounds on the approximation parameters of pushforward designs obtained from complex projective spaces, including simplices, mixed states, and quantum channels. In the mixed-state case, we refine the bounds by exploiting the symmetric subspace structure, leading to asymptotically tighter estimates. Numerical simulations support our theoretical results, showing near-optimality in low-dimensional scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01858 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate pushforward designs and image bounds on approximations Czartowski, Jakub Sawicki, Adam Życzkowski, Karol Quantum Physics Mathematical Physics We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten $p$-norms and Lipschitz continuity arguments, we derive bounds on the approximation parameters of pushforward designs obtained from complex projective spaces, including simplices, mixed states, and quantum channels. In the mixed-state case, we refine the bounds by exploiting the symmetric subspace structure, leading to asymptotically tighter estimates. Numerical simulations support our theoretical results, showing near-optimality in low-dimensional scenarios. |
| title | Approximate pushforward designs and image bounds on approximations |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2512.01858 |