2D Languages

Alex Wozniakowski, Zhengwei Liu, and Arthur Jaffe

New Insights into Quantum Information

With our 2-string model, we introduced a two-dimensional charged string language into quantum information. One of our main goals is to represent protocols using "picture A" of charged strings, and verify the function of the protocol (represented by a simplier "picture B" of charged strings) through braided paraisotopy between A and B.  More importantly, we can design new protocols using paraisotopy: we aim to realize a protocol whose function is represented by a picture B, although B may not be piecewise meaningful in quantum informaion. We apply paraisotopy to B to obtain a meaningful picture A that we can translate to realzable concepts in quantum information.  A and B are paraisotopic, but A is "real" and B is "virtual" in quantum information.

Previously in quantum information one could verify protocols using pictorial relations.  One main improvement in our approach is to understand protocols using paraisotopy. Furthermore, we can turn our method around to design protocols. Previous researchers usually used one string to represent a 1-qubit transformation, but we use 2 with charge. This provides additional power in using isotopy. It yields elementary pictures for Pauli matrices. We use a braid in this model, which allows us to use braid relations for charged strings. We also relate the ground state and the resource state in quantum information from a pictorial transformation that we call the string Fourier transform.

Arthur Jaffe, Zhengwei Liu, Alex Wozniakowski, Constructive Simulation and Topological Design of Protocols. arXiv: 1611.06447New Journal of Physics

Arthur Jaffe, Zhengwei Liu, Alex Wozniakowski, A New Diagrammatic Approach to Quantum Information. Preprint

Arthur Jaffe, Zhengwei Liu, Alex Wozniakowski, Holographic Software for Quantum Networks. arXiv: 1605.00127

Arthur Jaffe, Zhengwei Liu, Alex Wozniakowski. Qudit Isotopy. arxiV: 1602.02671

Arthur Jaffe and Zhengwei Liu, Planar Para Algebras, Reflection Positivity. arxiV: 1602.02662Commun. Math. Phys.

Pauli Matrices