Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation

In this work, we show how to parameterize a density matrix that has an arbitrary symmetry, knowing the generators of the Lie algebra (if the symmetry group is a connected Lie group) or the generators of its underlying group (in case it is finite). This allows to pose MaxEnt and MaxLik estimation techniques as convex optimization problems with a substantial reduction in the number of parameters of the function involved. This implies that, apart from a computational advantage due to the fact that the optimization is performed in a reduced space, the amount of experimental data needed for a good estimation of the density matrix can be reduced as well. In addition, we run numerical experiments and apply these parameterizations to estimate quantum states with different symmetries.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this work, the authors demonstrate a method for parameterizing density matrices with arbitrary symmetry. By utilizing the generators of the Lie algebra or the underlying group, the authors effectively reduce the parameter space for MaxEnt and MaxLik estimation techniques. This results in computational advantages and reduced data requirements for accurate estimation of the density matrix. The authors also conduct numerical experiments and apply the parameterizations to quantum states with different symmetries.