  Photon number states are assigned a parity of if their photon number is even
and a parity of if odd. The parity operator, which is minus one to the power of
the photon number operator, is a Hermitian operator and thus a quantum
mechanical observable though it has no classical analog, the concept being
meaningless in the context of classical light waves. In this paper we review
work on the application of the parity operator to the problem of quantum
metrology for the detection of small phase shifts with quantum optical
interferometry using highly entangled field states such as the so-called N00N
states, and states obtained by injecting twin Fock states into a beam splitter.
With such states and with the performance of parity measurements on one of the
output beams of the interferometer, one can breach the standard quantum limit,
or shot-noise limit, of sensitivity down to the Heisenberg limit, the greatest
degree of phase sensitivity allowed by quantum mechanics for linear phase
shifts. Heisenberg limit sensitivities are expected to eventually play an
important role in attempts to detect gravitational waves in interferometric
detection systems such as LIGO and VIRGO.
