  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. In the specific case where the
two subsystems are ensembles of two-level atoms or spins, our generalized
states define a notion of two-mode spin squeezing that is valid beyond the
Gaussian limit and that enables true multi-parameter estimation. We discuss how
generalized Ramsey measurements allow one to reach the two-parameter quantum
Cramer-Rao bound, and how the dissipative preparation scheme is compatible with
current experiments.
