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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2308.06245 |
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| _version_ | 1866910015737036800 |
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| author | Pandya, Palash |
| author_facet | Pandya, Palash |
| contents | The Hilbert-Schmidt distance between two states is proven to be non-contractive under CPTP maps, and therefore is not considered as an entanglement measure. However, that alone does not imply that the minimum Hilbert-Schmidt distance from the set of separable states is not contractive as well. To the contrary, not only do we provide a closed-form expression, we also provide analytical and numerical proof that minimum Hilbert-Schmidt distance for a given bipartite quantum state of Schmidt rank 2 is non-increasing under LOCC. The minimisation is taken to be over the set of separable states. We apply the algorithm by Verstraete et al [Journal of Modern Optics, 49(8), 2002] for the derivation of the analytical expression and Nielsen's theorem for the proof of monotonicity of the distance under LOCC. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06245 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimum Hilbert-Schmidt distance for Schmidt rank 2 states Pandya, Palash Quantum Physics The Hilbert-Schmidt distance between two states is proven to be non-contractive under CPTP maps, and therefore is not considered as an entanglement measure. However, that alone does not imply that the minimum Hilbert-Schmidt distance from the set of separable states is not contractive as well. To the contrary, not only do we provide a closed-form expression, we also provide analytical and numerical proof that minimum Hilbert-Schmidt distance for a given bipartite quantum state of Schmidt rank 2 is non-increasing under LOCC. The minimisation is taken to be over the set of separable states. We apply the algorithm by Verstraete et al [Journal of Modern Optics, 49(8), 2002] for the derivation of the analytical expression and Nielsen's theorem for the proof of monotonicity of the distance under LOCC. |
| title | Minimum Hilbert-Schmidt distance for Schmidt rank 2 states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.06245 |