Trace- and improved data processing inequalities for von Neumann algebras
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909176508186624 |
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| author | Hollands, Stefan |
| author_facet | Hollands, Stefan |
| contents | We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter et al. on finite dimensional density matrices, yields a bound how well a quantum state can be recovered after it has been passed through a channel. The natural applications of our results are in quantum field theory where the von Neumann algebras are known to be of type III. Along the way we generalize various multi-trace inequalities to general von Neumann algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_07479 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Trace- and improved data processing inequalities for von Neumann algebras Hollands, Stefan Mathematical Physics High Energy Physics - Theory Operator Algebras Quantum Physics We prove a version of the data-processing inequality for the relative entropy for general von Neumann algebras with an explicit lower bound involving the measured relative entropy. The inequality, which generalizes previous work by Sutter et al. on finite dimensional density matrices, yields a bound how well a quantum state can be recovered after it has been passed through a channel. The natural applications of our results are in quantum field theory where the von Neumann algebras are known to be of type III. Along the way we generalize various multi-trace inequalities to general von Neumann algebras. |
| title | Trace- and improved data processing inequalities for von Neumann algebras |
| topic | Mathematical Physics High Energy Physics - Theory Operator Algebras Quantum Physics |
| url | https://arxiv.org/abs/2102.07479 |