Computing coherence vectors and correlation matrices, with application to quantum discord quantification

TL;DR

This paper presents optimized methods for computing coherence vectors and correlation matrices in quantum systems, reducing computational complexity, with applications to quantum discord quantification and providing Fortran code for implementation.

Contribution

It introduces algebraic optimizations for calculating coherence vectors and correlation matrices, along with Fortran code for generalized Gell Mann matrices and quantum discord computation.

Findings

Reduced computational complexity through algebraic manipulations

Provided Fortran code for generalized Gell Mann matrices and vectors

Applied methods to Hilbert-Schmidt quantum discord calculation

Abstract

Coherence vectors and correlation matrices are important functions frequently used in physics. The numerical calculation of these functions directly from their definitions, which involves Kronecker products and matrix multiplications, may seem to be a reasonable option. Notwithstanding, as we demonstrate in this article, some algebraic manipulations before programming can reduce considerably their computational complexity. Besides, we provide Fortran code to generate generalized Gell Mann matrices and to compute the optimized and unoptimized versions of the associated Bloch's vectors and correlation matrix, in the case of bipartite quantum systems. As a code test and application example, we consider the calculation of Hilbert-Schmidt quantum discords.