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

CORTE, INÉS; LOSADA, MARCELO; TIELAS, DIEGO; HOLIK, FEDERICO; REBÓN, LORENA

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Año: 2023 vol. 611

0378-4371

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.