  We derive a computable analytical formula for the quantum fidelity between
two arbitrary multimode Gaussian states which is simply expressed in terms of
their first- and second-order statistical moments. We also show how such a
formula can be written in terms of symplectic invariants and used to derive
closed forms for a variety of basic quantities and tools, such as the Bures
metric, the quantum Fisher information and various fidelity-based bounds. Our
result can be used to extend the study of continuous-variable protocols, such
as quantum teleportation and cloning, beyond the current one-mode or two-mode
analyses, and paves the way to solve general problems in quantum metrology and
quantum hypothesis testing with arbitrary multimode Gaussian resources.
