  Collective measurements can project a system into an entangled state with
enhanced sensitivity for measuring a quantum phase, but measurement back-action
has limited previous efforts to only modest improvements. Here we use a
collective measurement to produce and directly observe, with no background
subtraction, an entangled, spin-squeezed state with phase resolution improved
in variance by a factor of 10.5(1.5), or 10.2(6) dB, compared to the initially
unentangled ensemble of N = 4.8 x 10^5 87Rb atoms. The measurement uses a
cavity-enhanced probe of an optical cycling transition to mitigate back-action
associated with state-changing transitions induced by the probe. This work
establishes collective measurements as a powerful technique for generating
entanglement for precision measurement, with potential impacts in biological
sensing, communication, navigation, and tests of fundamental physics.
