Quon 3D language for quantum information.
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 theC∗-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.
Harvard University, Cambridge, MA 02138.
Zhengwei
Z
Liu
Harvard University, Cambridge, MA 02138.
Alex
A
Wozniakowski
Harvard University, Cambridge, MA 02138 arthur_jaffe@harvard.edu.
Arthur M
AM
Jaffe
joint relation; picture-language; quantum information; quon language; topological algebra