Entanglement and Minimal Hilbert Space in the Classical Dual States of Quantum Theory

TL;DR

This paper explores the relationship between quantum entanglement and classicalization, showing that classicalization occurs under the Metaplectic group and analyzing entanglement in various states and topologies with potential experimental relevance.

Contribution

It introduces a new approach to dual classical states in quantum theory, analyzing entanglement under classicalization via the Metaplectic group and computing entanglement probabilities for different states.

Findings

Classicalization occurs under the Metaplectic group Mp(n).

Entanglement probabilities vary with state type and topology.

Theoretical results have potential experimental applications.

Abstract

A precise physical description and understanding of the classical dual content of quantum theory is necessary in many disciplines today: from concepts and interpretation to quantum technologies and computation. In this paper we investigate Quantum Entanglement with the new approach APL Quantum 2, 016104 (2025) on dual Classicalization. Thus, the results of this paper are twofold: Entanglement and Classicalization and the relationship between them. Classicalization truly occurs only under the action of the Metaplectic group Mp(n) (Minimal Representation group, double covering of the Symplectic group). Some of the results of this paper involves the computation and analysis of the entanglement for different types of coherent (coset and non coset) states and topologies: in the circle and the cylinder. We project the entangled wave functions onto the even (+) and odd (-) irreducible Hilbert Mp(n) subspaces, and compute their square norms: Entanglement Probabilities P++, P--, P+-, (eg in the same or in the different subspaces), and the Total sum of them, and more. These theoretical and conceptual results can be of experimental and practical real-world interest.