Quantum Entanglement, Quantum Teleportation, Multilinear Polynomials and Geometry

TL;DR

This paper introduces a geometric framework linking quantum entanglement and teleportation to multilinear polynomials and surface representations, offering new insights into quantum state geometry.

Contribution

It proposes a novel geometric representation of entangled states using non-factorable multilinear polynomials and draws analogies between quantum circuits and geometric transformations.

Findings

Bell states correspond to non-factorable multilinear polynomials

Quantum circuits are modeled as geometric transformations

Quantum teleportation is analogous to polynomial operations

Abstract

We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that the Bell's states are associated with non-factorable real multilinear polynomial, which can be represented geometrically by three-dimensional surfaces. Furthermore, in this framework, we show that a quantum circuit can be seen as a geometric transformations of plane geometry. This phenomenon is analogous to gravity, where matter curves space-time. In addition, we show an analogy between quantum teleportation and operations involving multilinear polynomials.