Non-Gaussian generalized two-mode squeezing: applications to two-ensemble spin squeezing and beyond

Bosonic two-mode squeezed states are paradigmatic entangled Gaussian states that have wide utility in quantum information and metrology. Here, we show that the basic structure of these states can be generalized to arbitrary bipartite quantum systems in a manner that allows simultaneous, Heisenberg-limited estimation of two independent parameters for finite-dimensional systems. Further, we show that these general states can always be stabilized by a relatively simple Markovian dissipative process even when pushing beyond the Gaussian limit. We study the specific case where the two subsystems are ensembles of two-level atoms, discuss how generalized Ramsey measurements allow one to achieve Heisenberg-limited sensitivity with the generalized two-mode squeezed state, and show that the dissipative preparation scheme is compatible with current experiments.