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

Author

Listed:
  • Corte, Inés
  • Losada, Marcelo
  • Tielas, Diego
  • Holik, Federico
  • Rebón, Lorena

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.

Suggested Citation

  • Corte, Inés & Losada, Marcelo & Tielas, Diego & Holik, Federico & Rebón, Lorena, 2023. "Parameterizing density operators with arbitrary symmetries to gain advantage in quantum state estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 611(C).
    • Handle: RePEc:eee:phsmap:v:611:y:2023:i:c:s0378437122009852
    DOI: 10.1016/j.physa.2022.128427
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    References listed on IDEAS

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    1. Vincenzo D'Ambrosio & Eleonora Nagali & Stephen P. Walborn & Leandro Aolita & Sergei Slussarenko & Lorenzo Marrucci & Fabio Sciarrino, 2012. "Complete experimental toolbox for alignment-free quantum communication," Nature Communications, Nature, vol. 3(1), pages 1-8, January.
    2. Thiago O. Maciel & André T. Cesário & Reinaldo O. Vianna, 2011. "Variational Quantum Tomography With Incomplete Information By Means Of Semidefinite Programs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(12), pages 1361-1372.
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