  We show how to use two-mode squeezed light to exponentially enhance
cavity-based dispersive qubit measurement. Our scheme enables true
Heisenberg-limited scaling of the measurement, and crucially, is not restricted
to small dispersive couplings or unrealistically long measurement times. It
involves coupling a qubit dispersively to two cavities, and making use of a
symmetry in the dynamics of joint cavity quadratures (a so-called
quantum-mechanics-free subsystem). We discuss the basic scaling of the scheme
and its robustness against imperfections, as well as a realistic implementation
in circuit quantum electrodynamics.
