Uncertainty relations based on state-dependent norm of commutator
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913625976864768 |
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| author | Mayumi, Aina Kimura, Gen Ohno, Hiromichi Chruściński, Dariusz |
| author_facet | Mayumi, Aina Kimura, Gen Ohno, Hiromichi Chruściński, Dariusz |
| contents | We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the Böttcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is strongly supported by numerical evidence. Both relations surpass the conventional Robertson and Schrödinger bounds, particularly as the quantum state becomes increasingly mixed. This reveals a previously undetected complementarity of quantum uncertainty, stemming from the non-commutativity of observables. We also compare our results with the Luo-Park uncertainty relation, demonstrating that our bounds can outperform especially for mutually unbiased observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12280 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uncertainty relations based on state-dependent norm of commutator Mayumi, Aina Kimura, Gen Ohno, Hiromichi Chruściński, Dariusz Quantum Physics We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the Böttcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is strongly supported by numerical evidence. Both relations surpass the conventional Robertson and Schrödinger bounds, particularly as the quantum state becomes increasingly mixed. This reveals a previously undetected complementarity of quantum uncertainty, stemming from the non-commutativity of observables. We also compare our results with the Luo-Park uncertainty relation, demonstrating that our bounds can outperform especially for mutually unbiased observables. |
| title | Uncertainty relations based on state-dependent norm of commutator |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.12280 |