  We propose and examine the use of biphoton pairs, such as those created in
parametric down conversion or four-wave mixing, to enhance the precision and
the resolution of measuring optical displacements by position-sensitive
detection. We show that the precision of measuring a small optical beam
displacement with this method can be significantly enhanced by the correlation
between the two photons, given the same optical mode. The improvement is
largest if the correlations between the photons are strong, and falls off as
the biphoton correlation weakens. More surprisingly, we find that the smallest
resolvable parameter of a simple split detector scales as the inverse of the
number of biphotons for small biphoton number ("Heisenberg scaling"), because
the Fisher information diverges as the parameter to be estimated decreases in
value. One usually sees this scaling only for systems with many entangled
degrees of freedom. We discuss the transition for the split-detection scheme to
the standard quantum limit scaling for imperfect correlations as the biphoton
number is increased. An analysis of an $N$-pixel detector is also given to
investigate the benefit of using a higher resolution detector. The physical
limit of these metrology schemes is determined by the uncertainty in the birth
zone of the biphoton in the nonlinear crystal.
