A Wozniakowski, and AM Jaffe, Quon 3D language for quantum information

Zhengwei Liu Harvard University, Vanderbilt University Alex Wozniakowski Harvard University Arthur M. Jaffe Harvard University

Mathematical Physics Quantum Algebra Spectral Theory and Operator Algebra mathscidoc:1705.22001

Distinguished Paper Award in 2017

PNAS, 114, (10), 2497-2502, 2017
We present a 3D topological picture-language for quantum information. Our approach combines charged excitations carried by strings, with topological properties that arise from embedding the strings in the interior of a 3D manifold with boundary. A quon is a composite that acts as a particle. Specifically, a quon is a hemisphere containing a neutral pair of open strings with opposite charge. We interpret multiquons and their transformations in a natural way. We obtain a type of relation, a string–genus “joint relation,” involving both a string and the 3D manifold. We use the joint relation to obtain a topological interpretation of the C* Hopf algebra relations, which are widely used in tensor networks. We obtain a 3D representation of the controlled NOT (CNOT) gate that is considerably simpler than earlier work, and a 3D topological protocol for teleportation.
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  title={A Wozniakowski, and AM Jaffe, Quon 3D language for quantum information},
  author={Zhengwei Liu, Alex Wozniakowski, and Arthur M. Jaffe},
Zhengwei Liu, Alex Wozniakowski, and Arthur M. Jaffe. A Wozniakowski, and AM Jaffe, Quon 3D language for quantum information. 2017. Vol. 114. In PNAS. pp.2497-2502. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530143415685019764.
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