A Quaternionic Map Causing Bipartite Entanglement

TL;DR

This paper introduces a novel quaternionic map that transforms a single quantum state into bipartite entanglement by embedding states in complex quaternions and exploiting their rotational properties.

Contribution

It defines the first quaternionic map capable of converting a single quantum state into bipartite entanglement, expanding the mathematical tools for quantum state manipulation.

Findings

The quaternionic map always induces bipartite entanglement under certain conditions.

Embedding quantum states in complex quaternions enables new transformations.

The method leverages quaternion rotations to control entanglement creation.

Abstract

In the following manuscript we propose a quaternionic map which transforms a single quantum state into a bipartite entanglement. Until now such a transformation has not been defined yet. To define such a map, we embed one particle state within the algebra of complex quaternions. Next, on the basis of rotational features of quaternions, we choose a special quaternion which in combination with a quaternion describing a particle state, causes its splitting in a specified direction in 4D space. Finally, we prove that the proposed operation, under several restrictions, always causes bipartite entanglement.