Tatiana Mihaescu†, Aurelian Isar‡
We present a short review on the subject of witnesses based on second moments as a primary tool for the efficient detection of entanglement and steering. In particular, we focus on the example of Gaussian states, which represent the core toolbox for the vast domain of continuous variable states. We fully define and characterise the entanglement and steering Gaussian witnesses, respectively, and then present a set of linear constraints as an alternative characterisation that allows for the implementation of a numerical optimisation semidefinite programming algorithm. We have the great pleasure to dedicate this paper in the honour of Professor Dan Tiba on the occasion of his 70th Anniversary and to wish him a long life in good health and further success in his scientific activity.
MSC: 81P40, 81P42
Keywords: witnesses based on second moments, entanglement witnesses, steering witnesses, Gaussian states, semidefinite programming
DOI 10.56082/annalsarscimath.2024.1.114
†mihaescu.tatiana@theory.nipne.ro Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania.
‡isar@theory.nipne.ro Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering, Bucharest-Magurele; Academy of Romanian Scientists, Bucharest, Romania.
The authors acknowledge the financial support received from the Romanian Ministry of Research, Innovation and Digitisation, through the Project PN 23 21 01 01/2023.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 16 no 1, 2024
