  We propose a multi-parameter quantum metrological protocol based on a
Mach-Zehnder interferometer with a squeezed vacuum input state and an
anti-squeezing operation at one of its output channels. A simple and intuitive
geometrical picture of the state evolution is provided by the marginal Wigner
functions of the state at each interferometer output channel. The protocol
allows to detect the value of the sum
$\beta=\frac{1}{2}(\varphi_1+\varphi_2)+\theta_\mathrm{in}-\theta_\mathrm{out}$,
of the relative phase $\theta_\mathrm{in}-\theta_\mathrm{out}$ between the two
squeezers, and the average of the phase delays $\varphi_1,\varphi_2$ in the two
arms of the interferometer. The detection sensitivity scales at the Heisenberg
limit and, remarkably, is robust to the detector inefficiency.
