  Quantum metrology enables estimation of optical phase shifts with precision
beyond the shot-noise limit. One way to exceed this limit is to use squeezed
states, where the quantum noise of one observable is reduced at the expense of
increased quantum noise for its complementary partner. Because shot-noise
limits the phase sensitivity of all classical states, reduced noise in the
average value for the observable being measured allows for improved phase
sensitivity. However, additional phase sensitivity can be achieved using phase
estimation strategies that account for the full distribution of measurement
outcomes. Here we experimentally investigate the phase sensitivity of a
five-particle optical spin-squeezed state generated by photon subtraction from
a parametric downconversion photon source. The Fisher information for all
photon-number outcomes shows it is possible to obtain a quantum advantage of
1.58 compared to the shot-noise limit, even though due to experimental
imperfection, the average noise for the relevant spin-observable does not
achieve sub-shot-noise precision. Our demonstration implies improved
performance of spin squeezing for applications to quantum metrology.
