Neutrinos as qubits and qutrits

TL;DR

This paper explores representing neutrinos as qubits and qutrits using the Poincaré sphere, enabling analysis of their entanglement properties and symmetries in quantum information theory.

Contribution

It introduces a novel mapping of neutrino states to qubit and qutrit systems, constructing the Poincaré sphere and entanglement measures for neutrino quantum states.

Findings

Constructed the Poincaré sphere for neutrino qubits and qutrits.

Calculated entanglement measures for neutrino qutrit systems.

Compared entanglement in bipartite qubit and qutrit neutrino systems.

Abstract

We map neutrinos to qubit and qutrit states of quantum information theory by constructing the Poincar\'e sphere using SU(2) Pauli matrices and SU(3) Gell-Mann matrices, respectively. The construction of the Poincar\'e sphere in the two-qubit system enables us to construct the Bloch matrix, which yields valuable symmetries in the Bloch vector space of two neutrino systems. By identifying neutrinos with qutrits, we calculate the measures of qutrit entanglement for neutrinos. We use SU(3) Gell-Mann matrices tensor products to construct the Poincar\'e sphere of two qutrits neutrino systems. The comparison between the entanglement measures of bipartite qubits and bipartite qutrits in the two neutrino system are shown. The result warrants a study of two qutrits entanglement in the three neutrino system.