  Broadband multidimensional variational measurement allows to overcome
Standard Quantum Limit (SQL) of a classical mechanical force detection,
resulting from quantum back action, which perturbs evolution of a mechanical
oscillator. In this optomechanic scheme detection of a resonant signal force
acting on a linear mechanical oscillator coupled to a system with three optical
modes with separation nearly equal to the mechanical frequency. The measurement
is performed by optical pumping of the central optical mode and measuring the
light escaping the two other modes. Detection of optimal quadrature components
of the optical modes and post processing result in the back action exclusion in
a broad frequency band and surpassing SQL. We show that optical losses inside
cavity restrict back action exclusion due to loss noise. We also analyze how
two-photon (nondegenerate) and conventional (degenerate) squeezing improve
sensitivity with account optical losses, considering mainly internal squeezing.
