Computing partial traces and reduced density matrices
Jonas Maziero · International Journal of Modern Physics C · 2016
Taking partial traces (PTrs) for computing reduced density matrices, or related functions, is a ubiquitous procedure in the quantum mechanics of composite systems. In this paper, we present a thorough description of this function and analyze the number of elementary operations (ops) needed, under some possible alternative implementations, to compute it on a classical computer. As we note, it is worthwhile doing some analytical developments in order to avoid making null multiplications and sums, what can considerably reduce the ops. For instance, for a bipartite system [Formula: see text] with dimensions [Formula: see text] and [Formula: see text] and for [Formula: see text], while a direct use of PTr definition applied to [Formula: see text] requires [Formula: see text] ops, its optimized implementation entails [Formula: see text] ops. In the sequence, we regard the computation of PTrs for general multipartite systems and describe Fortran code provided to implement it numerically. We also consider the calculation of reduced density matrices via Bloch’s parametrization with generalized Gell Mann’s matrices.