Equal-fidelity surface for a qubit state via equal-distance extended Bloch vectors and derivatives

TL;DR

This paper introduces an equal-fidelity surface in Bloch space for qubit states using a generalized Euclidean distance between extended Bloch vectors, linking it to other quantum state distances.

Contribution

It proposes a novel equal-distance measure for quantum states and characterizes an equal-fidelity surface in Bloch space based on this measure.

Findings

Defined a generalized Euclidean distance for extended Bloch vectors

Characterized an equal-fidelity surface in Bloch space

Connected the new distance to existing quantum state metrics

Abstract

We describe and characterize an equal-fidelity surface in Bloch space targeted for a qubit state by means of equal-distance concept. The distance is generalized and defined as the Euclidean distance between extended Bloch vectors for arbitrary dimensional states. The distance is a genuine distance according to the definition and is related to other distances between quantum states and super-fidelity.