Quantum α-z fidelity and α-z-weighted right mean

Abstract

In this paper, we establish some variational principles for the quantum [Formula: see text]-[Formula: see text]-fidelity. Then, we use quantum [Formula: see text]-[Formula: see text]-fidelity to measure the distance between two quantum orbits. We also study several properties of the [Formula: see text]-[Formula: see text]-weighted right mean which is the unique solution of the least squares problem with respect to the [Formula: see text]-[Formula: see text]-Bures Wasserstein distance. We show that the [Formula: see text]-[Formula: see text]-weighted right mean is a multivariate Lie–Trotter mean.