Abstract
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.
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