Momentum bispinor, two-qubit entanglement and twistor space

TL;DR

This paper explores the geometric and symmetry properties of momentum bispinors in Minkowski spacetime, linking them to two-qubit entanglement and twistor space, revealing new insights into their mathematical structure and physical interpretations.

Contribution

It introduces a novel geometric framework connecting momentum bispinors, twistor space, and quantum entanglement, providing new perspectives on their interrelations.

Findings

Geometry of entanglement via unit-energy hyperplane restriction

Analysis of Czachor's bispinor normalization and projection

Correspondence between momentum twistor submanifold and tachyonic particles

Abstract

We re-examine the symmetry structure of massive momentum bispinors in four dimensional Minkowski spacetime and apply the result to the geometry of a two-qubit entanglement system. The geometry of entanglement is recovered by restricting the momentum to unit-energy hyperplane inside the future light-cone. On a more formal side, to understand Czachor's alternative normalization of the bispinor and its projection property, we analyze the geometry of momentum twistor space. An interesting correpondence between a submanifold of the momentum twistor space and tachyonic particle is also investigated.