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arXiv · 2208.06540

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

Inés Corte·Marcelo Losada·Diego Tielas·Federico Holik·Lorena Rebón
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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.

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Inés Corte, Marcelo Losada, Diego Tielas, Federico Holik, Lorena Rebón. 2022-08-13. Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation. https://doi.org/10.1016/j.physa.2022.128427

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