Extended Tensor Products and Generalization of the Notion of Entanglement

TL;DR

This paper extends the mathematical concept of tensor products and entanglement beyond quantum physics, applying it to diverse fields like social sciences and non-Archimedean physics, enabling new interdisciplinary modeling approaches.

Contribution

It introduces a generalized framework for tensor products and entanglement, bridging quantum theory with social sciences and non-Archimedean physics.

Findings

Generalized entanglement concept applicable to various fields

Tensor products constructed for non-Archimedean and complex spaces

Potential for modeling in social sciences and physics

Abstract

Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and entanglement. We also study the relation between conventional entanglement of complex qubits and our generalized entanglement. Our construction can also be used to describe entanglement in the framework of non-Archimedean physics. It is also possible to construct tensor products of non-Archimedean (e.g., $p$-adic) and complex Hilbert spaces.