Gaussian tripartite entanglement in the simultaneous measurement of position and momentum

• Published in: Physics letters. A 2024-08, Vol.516, p.129653, Article 129653
• Main Authors: Mendoza-Fierro, J.A., Arévalo Aguilar, L.M.
• Format: Article
• Language: English
• Subjects: Continuous-variable cluster; Entanglement certification; Entanglement quantification; Gaussian entanglement; Simultaneous measurement
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2024.129653

By utilizing the positive partial transpose criterion, we certify Gaussian tripartite entanglement in the dynamics of the simultaneous measurement process of position and momentum raised by Arthurs and Kelly, considering a measurement configuration where the system under examination is a squeezed coherent state. Hence, the system is classified as a fully inseparable. Moreover, using the residual tripartite Rényi-2 entanglement as a quantifier measure, we determine the amount and behavior of the entanglement in the three-mode system as in all its reduced and global mode bipartitions. Besides, we compare the entanglement structure of the Arthurs-Kelly dynamics with that of the set of linear three-mode continuous-variable cluster states. The certification and quantification of entanglement in the simultaneous measurements process of the canonical pair pave the way for integrating this scheme into quantum information processing tasks. •Simultaneous measurement of a canonical pair can create Gaussian entanglement.•The Arthurs and Kelly model is a tripartite Gaussian entanglement generator.•The PPT criterion certifies Gaussian entanglement in the Arthurs-Kelly model.•The Hamiltonian of the simultaneous measurement creates a symmetric entanglement.•The entanglements of the Arthurs-Kelly dynamics and that of a three-mode linear continuous-variable cluster are compared.