The Quantum Perron-Frobenius Space
Operator Algebras
2023-06-21 v2 Mathematical Physics
Functional Analysis
math.MP
Quantum Algebra
Abstract
We introduce -positive elements in planar algebras. We establish the Perron-Frobenius theorem for -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.
Keywords
Cite
@article{arxiv.2305.18971,
title = {The Quantum Perron-Frobenius Space},
author = {Linzhe Huang and Arthur Jaffe and Zhengwei Liu and Jinsong Wu},
journal= {arXiv preprint arXiv:2305.18971},
year = {2023}
}
Comments
Some revisions have been made to Section 4