Fidelity of Mobius matrices related with Lorentz boosts

TL;DR

This paper explores the mathematical properties of Mobius matrices, showing they are equivalent to Lorentz boosts, and derives a formula for their fidelity using Lorentz gamma factors, linking quantum information and relativity.

Contribution

It provides an explicit formula for the fidelity of Mobius matrices based on Lorentz gamma factors, connecting quantum states with relativistic transformations.

Findings

Mobius matrices are normalized Lorentz boosts.

Fidelity of Mobius matrices expressed via Lorentz gamma factors.

Establishes a mathematical link between quantum states and Lorentz transformations.

Abstract

In this article we consider the extended version of a real counterpart of qubit density matrices, called the M\"obius matrix, and we see that it is a normalized Lorentz boost. Using the isomorphic gyrogroup structures between the set $\PP$ of all Lorentz boosts and the Einstein gyrogroup on the open unit ball $\B$ of $\R^n$ we give an explicit formula of the fidelity for M\"obius matrices in terms of Lorentz gamma factors.