Matrix product states and the decay of quantum conditional mutual information

• URL: http://arxiv.org/abs/2211.06794v2
• Date: Wed, 6 Mar 2024 06:06:05 GMT
• Title: Matrix product states and the decay of quantum conditional mutual information
• Authors: Pavel Svetlichnyy, Shivan Mittal and T.A.B. Kennedy
• Abstract summary: A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain. The quantum conditional mutual information (QCMI) is investigated and proved to be bounded by a function proportional to $exp(-q(|B|-K)+2K|B|)$, with $q$ and $K$ computable constants.
• Score: 0.16741831494720966
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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