Matrix product states and the decay of quantum conditional mutual information
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866913255402766336 |
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| author | Svetlichnyy, Pavel Mittal, Shivan Kennedy, T. A. B. |
| author_facet | Svetlichnyy, Pavel Mittal, Shivan Kennedy, T. A. B. |
| contents | A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain when the size of subsystem $B,$ denoted $|B|,$ is large enough. The quantum conditional mutual information (QCMI) is investigated and proved to be bounded by a function proportional to $\exp(-q(|B|-K)+2K\ln|B|)$, with $q$ and $K$ computable constants. The properties of the bounding function are derived by a new approach, with a corresponding improved value given for its asymptotic decay rate $q$. We show the improved value of $q$ to be optimal. Numerical investigations of the decay of QCMI are reported for a collection of matrix product states generated by selecting the defining isometry with respect to Haar measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_06794 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Matrix product states and the decay of quantum conditional mutual information Svetlichnyy, Pavel Mittal, Shivan Kennedy, T. A. B. Quantum Physics A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain when the size of subsystem $B,$ denoted $|B|,$ is large enough. The quantum conditional mutual information (QCMI) is investigated and proved to be bounded by a function proportional to $\exp(-q(|B|-K)+2K\ln|B|)$, with $q$ and $K$ computable constants. The properties of the bounding function are derived by a new approach, with a corresponding improved value given for its asymptotic decay rate $q$. We show the improved value of $q$ to be optimal. Numerical investigations of the decay of QCMI are reported for a collection of matrix product states generated by selecting the defining isometry with respect to Haar measure. |
| title | Matrix product states and the decay of quantum conditional mutual information |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2211.06794 |