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Holographic software for quantum networks

Arthur Jaffe Departments of Mathematics and Physics, Harvard University, Cambridge, MA, 02138, USA Zhengwei Liu Departments of Mathematics and Physics, Harvard University, Cambridge, MA, 02138, USA Alex Wozniakowski Present address: Current address: School of Physical and Mathematical Sciences and Complexity Institute, Nanyang Technological University, Singapore, 637723, Singapore; Departments of Mathematics and Physics, Harvard University, Cambridge, MA, 02138, USA

Mathematical Physics Quantum Algebra Spectral Theory and Operator Algebra arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.22002

Science China Mathematics, 61, 593–626, 2018.2
We introduce a pictorial approach to quantum information, called holographic software. Our software captures both algebraic and topological aspects of quantum networks. It yields a bi-directional dictionary to translate between a topological approach and an algebraic approach. Using our software, we give a topological simulation for quantum networks. The string Fourier transform (SFT) is our basic tool to transform product states into states with maximal entanglement entropy. We obtain a pictorial interpretation of Fourier transformation, of measurements, and of local transformations, including the n-qudit Pauli matrices and their representation by Jordan-Wigner transformations. We use our software to discover interesting new protocols for multipartite communication. In summary, we build a bridge linking the theory of planar para algebras with quantum information.
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@inproceedings{arthur2018holographic,
  title={Holographic software for quantum networks},
  author={Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703154658915763529},
  booktitle={Science China Mathematics},
  volume={61},
  pages={593–626},
  year={2018},
}
Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski. Holographic software for quantum networks. 2018. Vol. 61. In Science China Mathematics. pp.593–626. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220703154658915763529.
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