  The standard quantum limit constrains the precision of an oscillator position
measurement. It arises from a balance between the imprecision and the quantum
back-action of the measurement. However, a measurement of only a single
quadrature of the oscillator can evade the back-action and be made with
arbitrary precision. Here we demonstrate quantum back-action evading
measurements of a collective quadrature of two mechanical oscillators, both
coupled to a common microwave cavity. The work allows for quantum state
tomography of two mechanical oscillators, and provides a foundation for
macroscopic mechanical entanglement and force sensing beyond conventional
quantum limits.
