  We obtain universal (i.e., probe and measurement-independent) performance
bounds on ancilla-assisted quantum sensing of multiple parameters of
phase-covariant optical channels under energy and mode-number constraints. We
first show that for any such constrained problem, an optimal ancilla-entangled
probe can always be found whose reduced state on the modes probing the channel
is diagonal in the photon-number basis. For parameters that are encoded in
single-mode Gaussian channels, we derive a universal upper bound on the quantum
Fisher information matrix that delineates the roles played by the energy and
mode constraints. We illustrate our results for sensing of the transmittance of
a thermal loss channel under both the no-passive-signature and
passive-signature paradigms, and in the problem of sensing the noise variance
of an additive-noise channel. In both cases, we show that two-mode squeezed
vacuum probes are near-optimal under the constraints in the regime of low
signal brightness, i.e., per-mode average photon number. More generally, our
work sets down a uniform framework for readily evaluating universal limits for
any sensing problem involving Gaussian channels.
