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

TL;DR

This paper introduces a method to parameterize density matrices with arbitrary symmetries, enabling more efficient quantum state estimation by reducing parameters and data requirements through convex optimization.

Contribution

It provides a systematic way to incorporate symmetries into density matrix parameterization, improving quantum state estimation efficiency and accuracy.

Findings

Reduced number of parameters in estimation process

Decreased experimental data requirements

Successful numerical experiments with symmetric states

Abstract

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 quantum state estimation of states with different symmetries.