Symmetric Petz-Rényi relative entropy uncertainty relation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916112790192128 |
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| author | Salazar, Domingos S. P. |
| author_facet | Salazar, Domingos S. P. |
| contents | Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace norm. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace norm, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01390 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetric Petz-Rényi relative entropy uncertainty relation Salazar, Domingos S. P. Quantum Physics Statistical Mechanics Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as Holevo's inequality. More broadly, Holevo's fidelity is part of a one-parameter family of symmetric Petz-Rényi relative entropies, which in turn satisfy a Pinsker's-like inequality with respect to the trace norm. Although Holevo's inequality is tight, Pinsker's inequality is loose for this family. We show that the symmetric Petz-Rényi relative entropies satisfy a tight inequality with respect to the trace norm, improving Pinsker's and reproducing Holevo's as a specific case. Additionally, we show how this result emerges from a symmetric Petz-Rényi uncertainty relation, a result that encompasses several relations in quantum and stochastic thermodynamics. |
| title | Symmetric Petz-Rényi relative entropy uncertainty relation |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2402.01390 |