Error bounds for Lie Group representations in quantum mechanics
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909125530615808 |
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| author | van Luijk, Lauritz Galke, Niklas Hahn, Alexander Burgarth, Daniel |
| author_facet | van Luijk, Lauritz Galke, Niklas Hahn, Alexander Burgarth, Daniel |
| contents | We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated to the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy constrained diamond norm distance of any suitably continuous channel representation of the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08582 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Error bounds for Lie Group representations in quantum mechanics van Luijk, Lauritz Galke, Niklas Hahn, Alexander Burgarth, Daniel Quantum Physics Mathematical Physics We provide state-dependent error bounds for strongly continuous unitary representations of connected Lie groups. That is, we bound the difference of two unitaries applied to a state in terms of the energy with respect to a reference Hamiltonian associated to the representation and a left-invariant metric distance on the group. Our method works for any connected Lie group and the metric is independent of the chosen representation. The approach also applies to projective representations and allows us to provide bounds on the energy constrained diamond norm distance of any suitably continuous channel representation of the group. |
| title | Error bounds for Lie Group representations in quantum mechanics |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2211.08582 |