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arXiv · 2407.17621

Quantum Entanglement, Quantum Teleportation, Multilinear Polynomials and Geometry

Juan M. Romero·Emiliano Montoya-Gonzalez·Oscar Velazquez-Alvarado
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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.

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Juan M. Romero, Emiliano Montoya-Gonzalez, Oscar Velazquez-Alvarado. 2024-07-24. Quantum Entanglement, Quantum Teleportation, Multilinear Polynomials and Geometry. https://doi.org/10.1142/s0219887825502081

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