Quantum Entanglement, Quantum Teleportation, Multilinear Polynomials and Geometry

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.