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

Inés Corte, Marcelo Losada, Diego Tielas, Federico Holik and Lorena Rebón

Physica A: Statistical Mechanics and its Applications, 2023, vol. 611, issue C

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 estimate quantum states with different symmetries.

Keywords: Quantum state estimation; Group invariant quantum tomography; Variational quantum tomography; Quantum information theory; Symmetries; Density operators (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:611:y:2023:i:c:s0378437122009852

DOI: 10.1016/j.physa.2022.128427

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