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arXiv · 1605.00127

Holographic Software for Quantum Networks

Arthur Jaffe·Zhengwei Liu·Alex Wozniakowski
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Abstract

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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quant-phhep-thmath-phmath.MPmath.OAmath.QA

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BibTeXRIS

Arthur Jaffe, Zhengwei Liu, Alex Wozniakowski. 2016-04-30. Holographic Software for Quantum Networks. https://doi.org/10.1007/s11425-017-9207-3

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