Complexity in algebraic QFT
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918128011706368 |
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| author | Hollands, Stefan Ranallo, Alessio |
| author_facet | Hollands, Stefan Ranallo, Alessio |
| contents | We consider a notion of complexity of quantum channels in relativistic continuum quantum field theory (QFT) defined by the distance to the trivial (identity) channel. Our distance measure is based on a specific divergence between quantum channels derived from the Belavkin-Staszewski (BS) divergence. We prove in the prerequisite generality necessary for the algebras in QFT that the corresponding complexity has several reasonable properties: (i) the complexity of a composite channel is not larger than the sum of its parts, (ii) it is additive for channels localized in spacelike separated regions, (iii) it is convex, (iv) for an $N$-ary measurement channel it is $\log N$, (v) for a conditional expectation associated with an inclusion of QFTs with finite Jones index it is given by $\log (\text{Jones Index})$. The main technical tool in our work is a new variational principle for the BS divergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_10013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Complexity in algebraic QFT Hollands, Stefan Ranallo, Alessio Quantum Physics High Energy Physics - Theory Mathematical Physics Operator Algebras We consider a notion of complexity of quantum channels in relativistic continuum quantum field theory (QFT) defined by the distance to the trivial (identity) channel. Our distance measure is based on a specific divergence between quantum channels derived from the Belavkin-Staszewski (BS) divergence. We prove in the prerequisite generality necessary for the algebras in QFT that the corresponding complexity has several reasonable properties: (i) the complexity of a composite channel is not larger than the sum of its parts, (ii) it is additive for channels localized in spacelike separated regions, (iii) it is convex, (iv) for an $N$-ary measurement channel it is $\log N$, (v) for a conditional expectation associated with an inclusion of QFTs with finite Jones index it is given by $\log (\text{Jones Index})$. The main technical tool in our work is a new variational principle for the BS divergence. |
| title | Complexity in algebraic QFT |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics Operator Algebras |
| url | https://arxiv.org/abs/2302.10013 |