Matrix product states and the decay of quantum conditional mutual information
| Autor: | Svetlichnyy, Pavel, Mittal, Shivan, Kennedy, T. A. B. |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | J. Math. Phys. 1 February 2024; 65 (2): 022201 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/5.0152063 |
| Popis: | 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. Comment: 16+10 pages, 10 figures |
| Databáze: | arXiv |
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