Distances of qubit density matrices on Bloch sphere

Abstract

We recall the Einstein velocity addition on the open unit ball $\B$ of ${\mathbb{R}}^3$ and its algebraic structure, called the Einstein gyrogroup. We establish an isomorphism between the Einstein gyrogroup on $\B$ and the set of all qubit density matrices representing mixed states endowed with an appropriate addition. Our main result establishes a relation between the trace metric for the qubit density matrices and the rapidity metric on the Einstein gyrogroup $\B$.

I thank to my supervisor, Jimmie Lawson. This was accepted in Journal of Mathematical Physics at September 26, 2011

Cited by in corpus (4)

• Isomorphism Theorems for Gyrogroups and L-Subgyrogroups
• On algebraic endomorphisms of the Einstein gyrogroup
• Operator inequalities and gyrolines of the weighted geometric means
• On endomorphisms of the Einstein gyrogroup in arbitrary dimension