Coupled three-mode squeezed vacuum: Gaussian steering and remote generation of Wigner negativity

Multipartite Einstein-Podolsky-Rosen (EPR) steering and multimode quantum squeezing are essential resources for various quantum applications. The paper focuses on studying a coupled three-mode squeezed vacuum (C3MSV), which is a typical multimode squeezed Gaussian state and will exhibit peculiar steering property. Using the technique of integration within ordered products, we give the normal-ordering form for the coupled three-mode squeezing operator and derive the general analytical expressions of the statistical quantities for the C3MSV. Under Gaussian measurements, we analyze all bipartite Gaussian steerings (including no steering, one-way steering, and two-way steering) in detail and study the monogamy relations for the C3MSV. Then, we study the decoherence of all these steerings in noisy channels and find that sudden death will happen in a certain threshold time. Through the steerings shared in the C3MSV, we propose conceptual (and ideal) schemes of remotely generating Wigner negativity by performing appropriate photon subtraction(s) in the local position. Our obtained results may lay a solid theoretical foundation for a future practical study. We also believe that the C3MSV will be one of good candidate resources in future quantum protocols.