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arXiv · 2305.18971

The Quantum Perron-Frobenius Space

Linzhe Huang·Arthur Jaffe·Zhengwei Liu·Jinsong Wu
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Abstract

We introduce $\mathfrak{F}$-positive elements in planar algebras. We establish the Perron-Frobenius theorem for $\mathfrak{F}$-positive elements. We study the existence and uniqueness of the Perron-Frobenius eigenspace. When it is not one-dimensional, we characterize its multiplicative structure. Moreover, we consider the Perron-Frobenius eigenspace as the space of logical qubits for mixed states in quantum information. We describe the relation between these mathematical results and quantum error correction, especially to the Knill-Laflamme theorem.

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BibTeXRIS

Linzhe Huang, Arthur Jaffe, Zhengwei Liu, Jinsong Wu. 2023-05-30. The Quantum Perron-Frobenius Space. https://arxiv.org/abs/2305.18971

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