Generation and structuring of multipartite entanglement in Josephson parametric system

Quantum correlations are a vital resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for the generation of multipartite quantum entanglement. In this work, we achieve generation of genuine tripartite entangled state and its control by the use of the phase difference between two continuous pump tones. We demonstrate control of the subspaces of the covariance matrix for tripartite bisqueezed state. Furthermore, by optimizing the phase relationships in a three-tone pumping scheme we explore genuine quadripartite entanglement of a \textit{generalized} H-graph state ($\mathscr{\tilde{H}}$-graph). Our scheme provides a comprehensive control toolbox for the entanglement structure and allows us to demonstrate, for first time to our knowledge, genuine quadripartite entanglement of microwave modes. All experimental results are verified with numerical simulations of the nonlinear quantum Langevin equation. We envision that quantum resources facilitated by multi-pump configurations offer enhanced prospects for quantum data processing using parametric microwave cavities.