Teleportation of geometric structures in 3D

TL;DR

This paper presents a geometric algebra framework for quantum teleportation algorithms, offering a visual and algebraic alternative to traditional tensor-product representations, using colors and stereographic projection for clarity.

Contribution

It introduces a fully geometric representation of quantum teleportation, replacing tensor products with geometric algebra and color-based directed magnitudes.

Findings

Geometric analogs of quantum states and gates are developed.

A nonstandard color-based representation simplifies the geometric visualization.

The approach provides an alternative to tensor-product coding in quantum mechanics.

Abstract

Simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state-vectors) and 4 (for complex state-vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: Geometric analogs of states and controlled Pauli gates. Fully geometric presentation is possible if one employs a nonstandard representation of directed magnitudes, formulated in terms of colors defined via stereographic projection of a color wheel, and not by means of directed volumes.