Entanglement capabilities of the spin representation of (3+1)D-conformal transformations

TL;DR

This paper introduces the concept of intrinsic entanglement of spinors and investigates how conformal transformations in (3+1)D Minkowski space affect their entanglement capabilities, revealing that only certain tensor structures preserve non-entangled states.

Contribution

It establishes a novel concept of intrinsic entanglement for spinors and analyzes the entanglement capabilities of conformal transformations in four-dimensional spacetime.

Findings

Only specific tensor product structures allow for meaningful spinor entanglement.

Conformal transformations can alter the entanglement properties of spinors.

Certain structures preserve non-entangled states under transformations.

Abstract

Relying on a mathematical analogy of the pure states of the two-qubit system of quantum information theory with four-component spinors we introduce the concept of the intrinsic entanglement of spinors. To explore its physical sense we study the entanglement capabilities of the spin representation of (pseudo-) conformal transformations in (3+1)-dimensional Minkowski space-time. We find that only those tensor product structures can sensibly be introduced in spinor space for which a given spinor is not entangled.