  We present optimal schemes, based on photon number measurements, for Gaussian
state tomography and for Gaussian process tomography. An $n$-mode Gaussian
state is completely specified by $2 n^2+3n$ parameters. Our scheme requires
exactly $2 n^2+3n$ distinct photon number measurements to tomograph the state
and is therefore optimal. Further, we describe an optimal scheme to
characterize Gaussian processes by using coherent state probes and photon
number measurements. With much recent progress in photon number measurement
experimental techniques, we hope that our scheme will be useful in various
quantum information processing protocols including entanglement detection,
quantum computation, quantum key distribution and quantum teleportation. This
work builds upon the works of Parthasarathy et al. [Infin. Dimens. Anal.
Quantum Probab. Relat. Top., 18(4): 1550023, 21, 2015].
